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Kasztelan, Christian. "Strongly Interacting Quantum Systems out of Equilibrium." Diss., lmu, 2010. http://nbn-resolving.de/urn:nbn:de:bvb:19-124827.
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Antonio, R. G. "Quantum computation and communication in strongly interacting systems." Thesis, University College London (University of London), 2015. http://discovery.ucl.ac.uk/1469437/.
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Each year, the gap between theoretical proposals and experimental endeavours to create quantum computers gets smaller, driven by the promise of fundamentally faster algorithms and quantum simulations. This occurs by the combination of experimental ingenuity and ever simpler theoretical schemes. This thesis comes from the latter perspective, aiming to find new, simpler ways in which components of a quantum computer could be built. We first search for ways to create quantum gates, the primitive building blocks of a quantum computer. We find a novel, low-control way of performing a two-qubit gate on qubits encoded in a decoherence-free subspace, making use of many-body interactions that may already be present. This includes an analysis of the effect of control errors and magnetic field fluctuations on the gate. We then present novel ways to create three-qubit Toffoli and Fredkin gates in a single step using linear arrays of qubits, including an assessment of how well these gates could perform, for quantum or classical computation, using state-of-the-art ion trap and silicon donor technology. We then focus on a very different model from the normal circuit model, combining ideas from measurement-based quantum computation (MBQC) and holonomic quantum computation. We generalise an earlier model to show that all MBQC patterns with a property called gflow can be converted into a holonomic computation. The manifestation of the properties of MBQC in this adiabatically driven model is then explored. Finally, we investigate ways in which quantum information can be communicated between distant parties, using minimally engineered spin chains. The viability of using 1D Wigner crystals as a quantum channel is analysed, as well as schemes using ideal uniform spin chains with nextneighbour interactions, and edge-locking effects.
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Thomson, Steven. "The effects of disorder in strongly interacting quantum systems." Thesis, University of St Andrews, 2016. http://hdl.handle.net/10023/9441.
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This thesis contains four studies of the effects of disorder and randomness on strongly correlated quantum phases of matter. Starting with an itinerant ferromagnet, I first use an order-by-disorder approach to show that adding quenched charged disorder to the model generates new quantum fluctuations in the vicinity of the quantum critical point which lead to the formation of a novel magnetic phase known as a helical glass. Switching to bosons, I then employ a momentum-shell renormalisation group analysis of disordered lattice gases of bosons where I show that disorder breaks ergodicity in a non-trivial way, leading to unexpected glassy freezing effects. This work was carried out in the context of ultracold atomic gases, however the same physics can be realised in dimerised quantum antiferromagnets. By mapping the antiferromagnetic model onto a hard-core lattice gas of bosons, I go on to show the importance of the non-ergodic effects to the thermodynamics of the model and find evidence for an unusual glassy phase known as a Mott glass not previously thought to exist in this model. Finally, I use a mean-field numerical approach to simulate current generation quantum gas microscopes and demonstrate the feasibility of a novel measurement scheme designed to measure the Edwards-Anderson order parameter, a quantity which describes the degree of ergodicity breaking and which has never before been experimentally measured in any strongly correlated quantum system. Together, these works show that the addition of disorder into strongly interacting quantum systems can lead to qualitatively new behaviour, triggering the formation of new phases and new physics, rather than simply leading to small quantitative changes to the physics of the clean system. They provide new insights into the underlying physics of the models and make direct connection with experimental systems which can be used to test the results presented here.
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Carleo, Giuseppe. "Spectral and dynamical properties of strongly correlated systems." Doctoral thesis, SISSA, 2011. http://hdl.handle.net/20.500.11767/4289.
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In the first part of the Thesis we mostly concentrate on spectral properties of strongly correlated systems and on their equilibrium properties. This is accomplished by the general concept of imaginary-time dynamics which we apply to a number of different problems in which different strengths of this approach emerge.
In Chapter 1 we introduce the formalism that allows for a connection between the quantum and the classical worlds. The connection is established by means of the imaginary-time quantum evolution which, under certain circumstances, is shown to be equivalent to a classical stochastic process. It is further shown that exact static and spectral properties of correlated systems can be obtained when this mapping is feasible. The relationship between the imaginary-time dynamics in different frameworks such as the path-integral and the
perturbative one is also underlined.
In Chapter 2 we present a specific implementation of the general ideas previously presented. In particular we introduced an extension to lattice systems of the Reptation Monte Carlo algorithm [30] which benefits of a sampling scheme based on directed updates. Specific improvements over the existing methodologies consist in the unbiased evaluation of the imaginary-time path integrals for bosons and a systematic scheme to improve over the Fixed-node approximation for fermions. Applications to the Hubbard and the Heisenberg models are presented.
In Chapter 3 we demonstrate the application of the imaginary-time dynamics to the exact study of spectral properties. Subject of our attention is a highly anharmonic and correlated quantum crystal such as Helium 4 at zero temperature.[33] Concerning this system, we have obtained the first ab-initio complete phonon dispersion in good agreement with neutron spectroscopy experiments. Moreover, we have also studied the density excitations of solid
helium in a region of wave-vectors in between the collective (phonon) and the single-particle regimes, where the presence of residual coherence in the dynamics shows analogies between the highly anharmonic crystal and the superfluid phase.
In Chapter 4 we introduce a novel method, based on the imaginary-time dynamics, to obtain unbiased estimates of fermionic properties.[34] By means of this method and of a very accurate variational state, we provide strong evidence for the stability of a saturated ferromagnetic phase in the high-density regime of the two-dimensional infinite-U Hubbard model. By decreasing the electron density, we observe a discontinuous transition to a paramagnetic phase, accompanied by a divergence of the susceptibility on the paramagnetic side. This behavior, resulting from a high degeneracy among different spin sectors, is consistent with an infinite-order phase transition scenario.
In Chapter 5 the use of imaginary-time dynamics in the context of finite-temperature response functions is highlighted. As an application, we study an intriguing quantum phase featuring both glassy order and Bose-Einstein condensation. [35] We introduce and validate a model for the role of geometrical frustration in the coexistence of off-diagonal long range
order with an amorphous density profile. The exact characterization of the response of the system to an external density perturbation is what allows here to establish the existence of a spin-glass phase. The differences between such a phase and the otherwise insulating "Bose glasses" are further elucidated in the Chapter.
In the second part of the Thesis we focus our attention on the dynamics of closed systems out of equilibrium. This is accomplished by both non-stochastic exact methods for the dynamics and the introduction of a novel time-dependent Variational Monte Carlo scheme.
In Chapter 6 exact diagonalization schemes and renormalization-based methods for one-dimensional systems are introduced. We identify key phenomenological traits resulting from the many-body correlation in closed systems driven sufficiently away from equilibrium.[31]
We provide evidences that the dynamics of interacting lattice bosons away from equilibrium can be trapped into extremely long-lived inhomogeneous metastable states. The slowing down of incoherent density excitations above a threshold energy, much reminiscent of a dynamical arrest on the verge of a glass transition, is identified as the key feature of this phenomenon.
In Chapter 7 we present an extension to dynamical properties of the Variational Quantum Monte Carlo method.[32] This is accomplished by introducing a general class of time-dependent variational states which is based on the mapping of the many-body dynamics onto an instantaneous ground-state problem. The application of the method to the experimentally relevant quantum quenches of interacting bosons reveals the accuracy and the
reliability of the introduced numerical scheme. We indeed obtain for the first time a consistent variational description of the approach to the equilibrium of local observables and underline the origin of the metastability and glassy behavior previously identified.
In the very last part we draw our conclusions and show some possible paths for stimulating future research.
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Akhanjee, Shimul. "Classical and quantum aspects of strongly interacting one-dimensional systems." Diss., Restricted to subscribing institutions, 2008. http://proquest.umi.com/pqdweb?did=1679376391&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.
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Grover, Tarun Ph D. Massachusetts Institute of Technology. "Applied fractionalization : quantum phases and phase transitions of strongly interacting systems." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/68973.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2010.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 131-136).
Strongly correlated systems present interesting challenges in condensed matter physics. On the one hand, the theoretical work in the last two decades suggests that strong interactions may lead to new phases and phase transitions of matter that don't fit paradigms such as Fermi liquid theory or Landau's theory of phase transitions. On the other hand, there are actual materials which are undoubtedly governed by strong interactions and indeed do not fit the conventional paradigms but whose behavior often doesn't quite match our theoretical expectations. This gap between theory and experiments is slowly narrowing owing to the discovery of new materials and recent advances in numerical simulations. As an example, the material K - (ET)2Cu 2(CN) 3 exhibits metallic specific heat in its insulating phase. This is indicative of the theoretically proposed phenomena of 'fractionalization' where elementary excitations in a phase carry quantum numbers that are fractions of that corresponding to an electron. Similarly, there is growing numerical evidence of the theoretical phenomena of 'deconfined quantum criticality', where quantum Berry phases lead to emergence of fractionalized particles right at the phase transition. In this thesis we study phenomena where the concept of fractionalization is a useful tool to explore new phases and phase transitions. Most of our examples are in the context of frustrated quantum magnets. Along the way, we also explore topics such as quantum numbers of topological defects and non-abelian phases of matter. Whenever possible, we compare theoretical predictions with experimental and numerical data. We also discuss deconfined quantum criticality in the context of metallic systems where it opens the route to phase transitions very different from the conventional spin-density wave instability of Fermi surface.
by Tarun Grover.
Ph.D.
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Yan, Mi. "Quantum Dynamics of Strongly-Interacting Bosons in Optical Lattices with Disorder." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/87432.
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Ultracold atoms in optical lattices offer an important tool for studying dynamics in many-body interacting systems in a pristine environment. This thesis focuses on three theoretical works motivated by recent optical lattice experiments. In the first, we theoretically study the center of mass dynamics of states derived from the disordered Bose-Hubbard model in a trapping potential. We find that the edge states in the trap allow center of mass motion even with insulating states in the center. We identify short and long-time mechanisms for edge state transport in insulating phases. We also argue that the center of mass velocity can aid in identifying a Bose-glass phase. Our zero temperature results offer important insights into mechanisms of transport of atoms in trapped optical lattices while putting bounds on center of mass dynamics expected at non-zero temperature.
In the second work, we study the domain wall expansion dynamics of strongly interacting bosons in 2D optical lattices with disorder in a recent experiment {[}J.-y. Choi et al., Science 352, 1547 (2016)]. We show that Gutzwiller mean-field theory (GMFT) captures the main experimental observations, which are a result of the competition between disorder and interactions. Our findings highlight the difficulty in distinguishing glassy dynamics, which can be captured by GMFT, and many-body localization, which cannot be captured by GMFT, and indicate the need for further experimental studies of this system.
The last work features our study of phase diagrams of the 2D Bose-Hubbard model in an optical lattice with synthetic spin-orbit coupling. We investigate the transitions between superfluids with different phase patterns, which may be detected by measuring the spin-dependent momentum distribution.Ph. D.
Ultracold atoms in optical lattices, a periodic potential generated by laser beams, offer an important tool for quantum simulations in a pristine environment. Motivated by recent optical lattice experiments with the implementation of disorder and synthetic spin-orbit coupling, we utilize Gutzwiller mean-field theory (GMFT) to study the dynamics of disordered state in an optical lattice under the sudden shift of the harmonic trap, the domain wall expansion of strongly interacting bosons in 2D lattices with disorder, and spin-orbit-driven transitions in the Bose-Hubbard model. We argue that the center of mass velocity can aid in identifying a Bose-glass phase. Our findings show that evidence for many-body localization claimed in experiments [J.-y. Choi et al., Science 352, 1547 (2016)] must lie in the differences between GMFT and experiments. We also find that strong spin-orbit coupling alone can generate superfluids with finite momentum and staggered phase patterns.
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Shotter, Martin David. "The development of techniques to prepare and probe at single atom resolution strongly interacting quantum systems ot uitracold atoms." Thesis, University of Oxford, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.526117.
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Romanovsky, Igor Alexandrovich. "Novel properties of interacting particles in small low-dimensional systems." Diss., Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-07102006-041659/.
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Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2007.Landman, Uzi, Committee Member ; Yannouleas, Constantine, Committee Member ; Bunimovich, Leonid, Committee Member ; Chou, Mei-Yin, Committee Member ; Pustilnik, Michael, Committee Member.
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Czischek, Stefanie [Verfasser], and Thomas [Akademischer Betreuer] Gasenzer. "Simulating Strongly Interacting Quantum Spin Systems–From Critical Dynamics Towards Entanglement Correlations in a Classical Artificial Neural Network / Stefanie Czischek ; Betreuer: Thomas Gasenzer." Heidelberg : Universitätsbibliothek Heidelberg, 2019. http://d-nb.info/119790431X/34.
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NAVA, MARCO. "TWO DIMENSIONAL AND NOVEL QUASI TWO DIMENSIONAL QUANTUM LIQUIDS." Doctoral thesis, Università degli Studi di Milano, 2013. http://hdl.handle.net/2434/216307.
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In this thesis we have used Quantum Monte Carlo techniques to study two
systems that can be regarded as the archetype for neutral strongly interacting
systems: 4He, and its fermionic counterpart 3He.More specifically, we have used
the Path Integral Ground State and the Path Integral Monte Carlo methods to
study a system of two dimensional 3He (2d-3He) and a system of 4He adsorbed on
Graphene-Fluoride (GF) and Graphane (GH) at both zero and finite temperature.
The purpose of the study of 4He on GF (GH) was the research of new physical
phenomena, whereas in the case of 2d-3He it was the application of novel
methodologies for the ab-initio study of static and dynamic properties of Fermi
systems. In the case of 2d-3He we have computed the spin susceptibility as
function of density which turned out to be in very good agreement with
experimental data; we have also obtained the first ab-initio evaluation of the
zero-sound mode and the dynamic structure factor of 2d-3He that is in
remarkably good agreement with experiments. In the case of 4He adsorbed on GF
(GH), we determined the zero temperature equilibrium density of the first
monolayer of 4He showing also that the commensurate sqrt(3) x sqrt(3) R30 phase
is unstable on both substrates; at equilibrium density we found that 4He on GF
(GH) is a modulated superfluid with an anisotropic phono-rotonic spectrum; at
high coverages we found an incommensurate triangular solid and, on both GF and
GH, a commensurate phase at filling factor x= 2/7 that is locally stable or at
least metastable. Remarkably, in this commensurate solid phase and for both GF
and GH, our computations show preliminary evidence of the presence of a
superfluid fraction.
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Botzung, Thomas. "Study of strongly correlated one-dimensional systems with long-range interactions." Thesis, Strasbourg, 2019. http://www.theses.fr/2019STRAF062.
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Durant cette thèse, nous étudions des systèmes unidimensionnels avec des couplages longue-portée. Dans la première partie, nous démontrons que ces couplages entraînent une décroissance algébrique des corrélations dans des fils quantiques désordonnés. Deuxièmement, nous analysons un modèle étendu de Hubbard où les particules interagissent via un potentiel « soft-core » générant de nouvelles phases exotiques. Dans le troisième chapitre, nous démontrons que restaurer l’extensivité a une influence sur les propriétés de basse énergie de modèle quantique dans la limite thermodynamique. Finalement, nous présentons des résultats préliminaires sur la modification de la localisation d’Anderson en présence d’un couplage avec une cavitéDuring this Ph.D., we studied one-dimensional systems with long-range couplings. In the first part, we demonstrate that power-law couplings lead to an algebraic decay of correlations at long distances in disordered quantum wires. In the second chapter, we analysed an extended Hubbard model where particles interact via a finite-range potential that induces frustration and new exotic phases. In the third chapter, we demonstrated that restoring energy extensivity has an influence on the low-energy properties of quantum model in the thermodynamic limit. Finally, we provide preliminary results on the modification of Anderson localization due to the coupling to a cavity mode
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Dobrautz, Werner [Verfasser], and Ali [Akademischer Betreuer] Alavi. "Development of full configuration interaction quantum Monte Carlo methods for strongly correlated electron systems / Werner Dobrautz ; Betreuer: Ali Alavi." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2019. http://d-nb.info/1197056459/34.
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Wu, Cheng-Hsun Ph D. Massachusetts Institute of Technology. "Strongly interacting quantum mixtures of ultracold atoms." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/83817.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2013.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 198-202).
This thesis describes the construction of a new apparatus for ultracold quantum gases as well as the scientific results this machine has produced so far. This new apparatus is capable of simultaneously cooling and trapping lithium, sodium, and potassium. It therefore provides a platform to study a large variety of quantum mixtures. Three main experimental results are presented. Firstly, the direct cooling of "K to Bose-Einstein condensation is presented. Then the 41K atoms provide the coolant for 6Li and 40K, achieving a triply degenerate gas of 6Li -40K -41K. In particular, a broad interspecies Feshbach resonance between 40K -41K is observed, opening a new pathway to study a strongly interacting isotopic Bose-Fermi mixture of 40K -41K. Secondly, a new Bose-Fermi mixture of 23Na -40K is introduced. We show that 23Na is a very efficient coolant for 40K by sympathetically cooling 40K to quantum degeneracy with the help of a 23Na condensate. Moreover, over thirty interspecies Feshbach resonances are identified, paving the way to study strongly interacting Bose- Fermi problems, in particular the Bose polaron problem. Thirdly, we report on the first formation of ultracold fermionic Feshbach molecules of 23Na40K by radio-frequency association. The lifetime of the nearly degenerate molecular gas exceeds 100 ms in the vicinity of the Feshbach resonance. The NaK molecule features chemical stability in its ground state in contrast to the case of the KRb molecule. Therefore, our work opens up the prospect of creating chemically stable, fermionic ground state molecules of 23Na40K where strong, long-range dipolar interactions will set the dominant energy scale. Finally, the thesis concludes with an outlook on future topics in polaron physics and quantum dipolar gases, which can be studied using the new apparatus.
by Cheng-Hsun Wu.
Ph.D.
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Jäckel, Jörg. "Effective actions for strongly interacting fermionic systems." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=968788351.
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Pugh, Emma. "Pressure studies on strongly interacting electron systems." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621542.
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O'Connell, Heath B. "Vector meson models of strongly interacting systems /." Title page, abstract and table of contents only, 1996. http://web4.library.adelaide.edu.au/theses/09PH/09pho175.pdf.
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Williams, Ceri Rhys. "Quantum interacting branching systems." Thesis, University of Nottingham, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.416728.
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Mia, Mohammed Shahpur. "Vector meson properties in a strongly interacting thermal medium." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=101626.
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We analyze the hadronic phase of QCD using effective thermal field theory techniques. Our goal is to investigate the medium created in heavy ion collisions by calculating the electromagnetic emissivity of strongly interacting matter in the hadronic phase. We proceed through examining the vector meson properties in a thermal bath where the temperature reaches deconfinement and chiral symmetry is restored. In particular we observe the behavior of the rho spectral function in thermal medium and use it as a probe to examine the thermal environment generated in the collision.
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Gasbarro, Andrew David. "Studies of Conformal Behavior in Strongly Interacting Quantum Field Theories." Thesis, Yale University, 2019. http://pqdtopen.proquest.com/#viewpdf?dispub=13851872.
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In this dissertation, we present work towards characterizing various conformal and nearly conformal quantum field theories nonperturbatively using a combination of numerical and analytical techniques. A key area of interest is the conformal window of four dimensional gauge theories with Dirac fermions and its potential applicability to beyond the standard model physics.
In the first chapter, we review some of the history of models of composite Higgs scenarios in order to motivate the study of gauge theories near the conformal window. In the second chapter we review lattice studies of a specific theory, SU(3) gauge theory with eight flavors of Dirac fermions in the fundamental representation of the gauge group. We place a particular emphasis on the light flavor-singlet scalar state appearing in the spectrum of this model and its possible role as a composite Higgs boson. We advocate an approach to characterizing nearly conformal gauge theories in which lattice calculations are used to identify the best low energy effective field theory (EFT) description of such nearly conformal gauge theories, and the lattice and EFT are then used as complementary tools to classify the generic features of the low energy physics in these theories. We present new results for maximal isospin ππ → ππ scattering on the lattice computed using Lüscher's finite volume method. This scattering study is intended to provide further data for constraining the possible EFT descriptions of nearly conformal gauge theory. In Chapter 3, we review the historical development of chiral effective theory from current algebra methods up through the chiral Lagrangian and modern effective field theory techniques. We present a new EFT framework based on the linear sigma model for describing the low lying states of nearly conformal gauge theories. We place a particular emphasis on the chiral breaking potential and the power counting of the spurion field.
In Chapter 4, we report on a new formulation of lattice quantum field theory suited for studying conformal field theories (CFTs) nonperturbatively in radial quantization. We demonstrate that this method is not only applicable to CFTs, but more generally to formulating a lattice regularization for quantum field theory on an arbitrary smooth Riemann manifold. The general procedure, which we refer to as quantum finite elements (QFE), is reviewed for scalar fields. Chapter 5 details explicit examples of numerical studies of lattice quantum field theories on curved Riemann manifolds using the QFE method. We discuss the spectral properties of the finite element Laplacian on the 2-sphere. Then we present a study of interacting scalar field theory on the 2-sphere and show that at criticality it is in close agreement with the exact c = 1/2 minimal Ising CFT to high precision. We also investigate interacting scalar field theory on [special characters omitted] x [special characters omitted]2, and we report significant progress towards studying the 3D Ising conformal fixed point in radial quantization with the QFE method. In the near future, we hope for the QFE method to be used to characterize the four dimensional conformal fixed points considered in the first half of this dissertation.
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Fearon, Michael. "Theoretical studies of strongly interacting fine particle systems." Thesis, University of Central Lancashire, 1990. http://clok.uclan.ac.uk/20347/.
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A theoretical analysis of the time dependent behaviour of a system of fine magnetic particles as a function of applied field and temperature was carried out. The model used was based on a theory assuming Neel relaxation with a distribution of particle sizes. This theory predicted a linear variation of 5max with temperature and a finite intercept, which is not reflected by experimental observations. The remanence curves of strongly interacting fine-particle systems were also investigated theoretically. It was shown that the Henkel plot of the dc demagnetisation remanence vs the isothermal remanence is a useful representation of interactions. The form of the plot was found to be a reflection of the magnetic and physical microstructure of the material, which is consistent with experimental data. The relationship between the Henkel plot and the noise of a particulate recording medium, another property dependent on the microstructure, is also considered. The Interaction Field Factor (1FF), a single parameter characterising the non-linearity of the Henkel plot, is investigated. These results are consistent with a previous experimental study. Finally the results of the noise power spectral density for erased and saturated recording media are presented, so that characterisation of interparticle interactions may be carried out with greater accuracy.
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Bienias, Przemysław [Verfasser]. "Few-body quantum physics with strongly interacting Rydberg polaritons / Przemysław Bienias." München : Verlag Dr. Hut, 2017. http://d-nb.info/1147674302/34.
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Fehrmann, Henning. "Strongly correlated systems in ultracold quantum gases." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=981637442.
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Shevchenko, Pavel Physics Faculty of Science UNSW. "Quantum Phenomena in Strongly Correlated Electrons Systems." Awarded by:University of New South Wales. Physics, 1999. http://handle.unsw.edu.au/1959.4/32669.
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Quantum phenomena in high-Tc superconductors and dimerized quantum Heisenberg antiferromagnets are studied analytically in this thesis. The implications of the Fermi surface consisting of the disjoint pieces, observed in cuprate superconductors, are considered. It is demonstrated that in this case the g-wave superconducting pairing is closely related to d-wave pairing. The superconductivity in this system can be described in terms of two almost degenerate superconducting condensates. As a result a new spatial scale lg, much larger than the superconducting correlation length x, arises and a new collective excitation corresponding to the relative phase oscillation between condensates, the phason, should exist. The Josephson tunneling for such a two-component system has very special properties. It is shown that the presence of g-wave pairing does not contradict the existing SQUID experimental data on tunneling in the ab-plane. Possible ways to experimentally reveal the g-wave component and the phason in a single tunnel junction, as well as in SQUID experiments, are discussed. The dimerized quantum spin models studied in this thesis include double-layer and alternating chain Heisenberg antiferromagnets. To account for strong correlations between the S=1 elementary excitations (triplets) in the dimerized phase; the analytic Brueckner diagram approach based on a description of the excitations as triplets above a strong-coupling singlet ground state; has been applied. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Analytical calculations of physical observables are in excellent agreement with numerical data.Results obtained for double layer antiferromagnet near the (zero temperature) quantum critical point coincide with those previously obtained within the nonlinear s model approach Additional singlet (S=0) and triplet (S=1) modes are found as two-particle bound states of the elementary triplets in the Heisenberg chain with frustration.
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Ye, Bing. "Unconventional Quantum Phases in Strongly Correlated Systems." Thesis, Boston College, 2016. http://hdl.handle.net/2345/bc-ir:106990.
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Thesis advisor: Ying RanIn this thesis, I investigated and implemented various numerical and simulation methods, including mean field theory, functional renormalization group method (fRG), density matrix renormalization group (DMRG) method etc., to find different quantum phases and quantum phase diagrams on models of correlated electronic systems. I found different phase diagrams with phases such as magnetism, superconductivity. By summarizing the strength and limitations of these methods, I investigated the projected entangled paired states (PEPS) with symmetry quantum number to sharply distinguish phases into crude classes and applied a variation of fast full update (FFU) prototype[58] to simulate different phases numerically. This method provides a promising, powerful and efficient way to simulate unconventional quantum phases and quantum phase diagrams in correlated electronic systems
Thesis (PhD) — Boston College, 2016
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Physics
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Manmana, Salvatore Rosario. "Nonequilibrium dynamics of strongly correlated quantum systems." [S.l. : s.n.], 2006. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-29095.
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Iles-Smith, Jake. "Excitation dynamics of strongly dissipative quantum systems." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/33203.
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Strong coupling between a quantum system and its many-body environment is becoming an increasingly important topic for many branches of physics. Numerous systems of experimental and technological relevance demonstrate strong system-environment coupling, leading to complex dynamical behaviour. This thesis is concerned with two particular examples of such systems, namely quantum dots (QDs) and excitonic energy transfer (EET) in molecular systems. Traditional quantum optics treatments are often insufficient to describe the transient, steady state, and optical properties of QDs due to system-environment correlations. In contrast, we present a modified theory of quantum optics capable of capturing the influence of a thermal environment on the behaviour of QDs. Using this framework we demonstrate a striking departure of the emission spectra and photon measurement statistics of a classically driven QD when compared to an analogous atomic system. Furthermore, in contradiction to accepted notions of decoherence and dissipation, we show that the interaction between a QD and its thermal environment induces non-classical light-matter correlations in an otherwise semi-classical regime of cavity quantum electrodynamics. Away from QDs, we develop the reaction coordinate (RC) formalism to describe the dynamics of a system coupled to a low frequency environment - a regime important to EET systems. We do so by identifying and incorporating important environmental degrees of freedom into an enlarged system Hamiltonian. Uniquely, this approach gives insight directly into the dynamical evolution of the environment and correlations accumulated between the system and environment. Furthermore, it is demonstrated that these corre- lations persist into the steady state, generating non-canonical equilibrium states of the system and environment. We then apply the RC model to describe EET in a molecular dimer, highlighting the effect that under- and over-damped environments have on the excitation dynamics. In doing so, we show interactions between the dimer and a structured environment can significantly enhance the energy transfer rate.
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Bennett, Edward. "Physical and computational applications of strongly-interacting dynamics beyond QCD." Thesis, Swansea University, 2013. https://cronfa.swan.ac.uk/Record/cronfa38186.
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In this thesis we investigate numerically SU(2) theories with Dirac—or Majorana—fermions in the adjoint representation. Majorana fermions have historically proven difficult to treat numerically; here, a change of basis is introduced that allows two Majorana fermions to be expressed in terms of one Dirac fermion. This also provides greater insight into the analysis of the properties of theories with Dirac fermions. Attention is focused on the SU(2) theory with a single Dirac flavour (or equivalently two Majorana flavours). Its lattice phase diagram, spectrum, and the anomalous dimension of the chiral condensate are investigated. We observe a long region of constant mass ratios and an anomalous dimension 0.9 ≲ γ∗ ≲ 0.95. The behaviour of the pion mass and the presence of a light scalar in particular point to behaviour that is not traditionally confining; instead the theory appears to lie in or near the conformal window. The topological susceptibility and instanton size distribution are also investigated, for the one-Dirac-flavour theory and additionally the pure-gauge and two-Dirac-flavour (Minimal Walking Technicolor) theories. The properties are found to not depend on number of flavours, indicating a quenching of the fermions in the topology, also consistent with (near-)conformal behaviour (as has previously been reported in studies of other observables for Minimal Walking Technicolor). The code used is described, and a high-performance computing benchmark developed from it is detailed. While the benchmark was originally developed to investigate the performance of different supercomputer architectures for the class of problems we are interested in. Due to the nature of the code on which it is based, it has an unusual flexibility in the demands it may place on machine’s performance characteristics, which may allow it to be applicable to problems outside of lattice physics. The benchmark is used to characterise a number of machines’ relative performance.
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Stellin, Filippo. "Anderson localization in interacting quantum systems." Thesis, Université de Paris (2019-....), 2020. http://www.theses.fr/2020UNIP7004.
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Dans cette thèse nous étudions au niveau théorique le comportement des particules quantiques (électrons, atomes, photons, etc.) se mouvant dans un milieu désordonné et sujets à la localisation d’Anderson. Pour des particules non interagissantes, le spectre de l’énergie peut posséder un ou plus points critiques, où les fonctions d’onde étendues deviennent localisées, en donnant lieu à une transition de phase métal-isolant connue comme Transition d’Anderson.Une question fondamentale est si et comment les transitions d’Anderson survivent dans des systèmesquantiques interagissants. Dans cet ouvrage, nous étudions un modèle simple décrivant le cas de deux particules dans un réseau désordonné et sujettes à des interactions mutuelles à courte portée. En combinant des simulations numériques sur une grande échelle avec des techniques à la fonction de Green, nous montrons que les transitions d’Anderson à deux particules se produisent en trois dimensions et explorons le diagramme de phase dans l’espace de l’énergie, du désordre et de l’interaction.Cette dernière présente une structure riche, caractérisée par un double renfoncement de la limite de phase, engendrée par la compétition entre les états de diffusion et les états liés de la paire. Nous prouvons aussi que les annonces précédentes concernant l’apparition de transitions d’Anderson en deux dimensions étaient essentiellement dues à des effets de taille finie.Un deuxième problème que nous abordons dans cette thèse est celui de l’occurrence de transitions métal-isolant en deux dimensions pour une particule en la présence d’un potentiel spatialement corrélé et sujette à des interactions spin-orbite, modélisées par les couplages Rashba-Dresselhaus. On éclaire que, indépendamment des propriétés du désordre, il y a un régime où l’énergie critique dépend linéairement du paramètre de désordre. La pente et l’intercepte sont étudiées en voisinage du point de symétrie spin-hélice persistant, dans lequel la symétrie SU(2) est restaurée et la transition métal-isolant disparaîtIn this thesis we theoretically investigate the behaviour of quantum particles (electrons, atoms, photons, etc.) moving in a random medium and undergoing Anderson localization. For noninteractingparticles, the energy spectrum can possess one or more critical points, where the nature of the single-particle wavefunctions changes from extended to localized leading to a undergoes a metal-insulator phase transition, also known as Anderson transition.A fundamental question is whether and how Anderson transitions survive in interacting quantum systems. Here we study a minimal model of two particles moving in a disordered lattice and subject to short-range mutual interactions. By combining large-scale numerics with Green’s functions techniques, we show that two-particle Anderson transitions do occur in three dimensions and explore the phase diagram in the space of energy, disorder and interaction strength. The latter presents a rich structure, characterized by a doubly reentrant behavior, caused by the competition between scattering and bound states of the pair. We also show that previous claims of 2D Anderson transitions of the pair are essentially due to finite-size effects.A second problem that we address in this thesis is the occurrence of 2D metal-insulator transitions for a single particle in the presence of a spatially correlated potential and subject to spin-orbit interactions, described by Rashba-Dresselhaus couplings. We illustrate that, irrespective of the properties of the disorder, there is a regime where the critical energy depends linearly on the disorder strength. The slope and the intercept are studied in the vicinity of the spin-helix point, where the SU(2) symmetry is restored and the 2D metal-insulator transition disappears
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Klugkist, Joost André. "Mechanisms for photonic switching in systems of strongly interacting dipoles." [S.l. : [Groningen : s.n.] ; University Library Groningen] [Host], 2008. http://irs.ub.rug.nl/ppn/306046253.
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Bayani, Babak [Verfasser]. "Interacting quantum-dissipative tunnelling systems / Babak Bayani." Mainz : Universitätsbibliothek Mainz, 2012. http://d-nb.info/1019453125/34.
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Bonnet, Jacqueline A. [Verfasser]. "Phase transitions in strongly interacting quantum field theories: QED_3 vs. QCD / Jacqueline A. Bonnet." Gießen : Universitätsbibliothek, 2013. http://d-nb.info/1065462670/34.
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Bridgeman, Jacob. "Tensor Network Methods for Quantum Phases." Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/17647.
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The physics that emerges when large numbers of particles interact can be complex and exotic. The collective behaviour may not re ect the underlying constituents, for example fermionic quasiparticles can emerge from models of interacting bosons. Due to this emergent complexity, manybody phenomena can be very challenging to study, but also very useful. A theoretical understanding of such systems is important for robust quantum information storage and processing. The emergent, macroscopic physics can be classi ed using the idea of a quantum phase. All models within a given phase exhibit similar low-energy emergent physics, which is distinct from that displayed by models in di erent phases. In this thesis, we utilise tensor networks to study many-body systems in a range of quantum phases. These include topologically ordered phases, gapless symmetry-protected phases, and symmetry-enriched topological phases.
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Liu, Jun. "Quantum phases in frustrated strongly correlated 2-D systems." [Ames, Iowa : Iowa State University], 2007.
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Kriel, Johannes Nicolaas. "A duality construction for interacting quantum Hall systems." Thesis, Stellenbosch : University of Stellenbosch, 2011. http://hdl.handle.net/10019.1/6749.
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Thesis (PhD)--University of Stellenbosch, 2011.ENGLISH ABSTRACT: The fractional quantum Hall effect represents a true many-body phenomenon in which the collective behaviour of interacting electrons plays a central role. In contrast to its integral counterpart, the appearance of a mobility gap in the fractional quantum Hall regime is due entirely to the Coulomb interaction and is not the result of a perturbed single particle gap. The bulk of our theoretical understanding of the underlying many-body problem is based on Laughlin’s ansatz wave function and the composite fermion picture proposed by Jain. In the latter the fractional quantum Hall effect of interacting electrons is formulated as the integral quantum Hall effect of weakly interacting quasiparticles called composite fermions. The composite fermion picture provides a qualitative description of the interacting system’s low-energy spectrum and leads to a generalisation of Laughlin’s wave functions for the electron ground state. These predictions have been verified through extensive numerical tests. In this work we present an alternative formulation of the composite fermion picture within a more rigorous mathematical framework. Our goal is to establish the relation between the strongly interacting electron problem and its dual description in terms of weakly interacting quasiparticles on the level of the microscopic Hamiltonian itself. This allows us to derive an analytic expression for the interaction induced excitation gap which agrees very well with existing numerical results. We also formulate a mapping between the states of the free particle and interacting descriptions in which the characteristic Jastrow-Slater structure of the composite fermion ansatz appears naturally. Our formalism also serves to clarify several aspects of the standard heuristic construction, particularly with regard to the emergence of the effective magnetic field and the role of higher Landau levels. We also resolve a long standing issue regarding the overlap of unprojected composite fermion trial wave functions with the lowest Landau level of the free particle Hamiltonian.
AFRIKAANSE OPSOMMING: Die fraksionele kwantum Hall-effek is ’n veeldeeltjie verskynsel waarin die kollektiewe gedrag van wisselwerkende elektrone ’n sentrale rol speel. In teenstelling met die heeltallige kwantum Hall-effek is die ontstaan van ’n energie gaping in die fraksionele geval nie ’n enkeldeeltjie effek nie, maar kan uitsluitlik aan die Coulomb wisselwerking toegeskryf word. Die teoretiese raamwerk waarbinne hierdie veeldeeltjie probleem verstaan word is grootliks gebaseer op Laughlin se proefgolffunksie en die komposiete-fermion beeld van Jain. In laasgenoemde word die fraksionele kwantum Hall-effek van wisselwerkende elektrone geformuleer as die heeltallige kwantum Hall-effek van swak-wisselwerkende kwasi-deeljies wat as komposiete-fermione bekend staan. Hierdie beeld lewer ’n kwalitatiewe beskrywing van die wisselwerkende sisteem se lae-energie spektrum en lei tot ’n veralgemening van Laughlin se golffunksies vir die elektron grondtoestand. Hierdie voorspellings is deur verskeie numeriese studies geverifieer. In hierdie tesis ontwikkel ons ’n alternatiewe formulering van die komposiete-fermion beeld binne ’n strenger wiskundige raamwerk. Ons doel is om die verband tussen die sterk-wisselwerkende elektron sisteem en sy duale beskrywing in terme van swak-wisselwerkende kwasi-deeltjies op die vlak van die mikroskopiese Hamilton-operator self te realiseer. Hierdie konstruksie lei tot ’n analitiese uitdrukking vir die opwekkingsenergie wat baie goed met bestaande numeriese resultate ooreenstem. Ons identifiseer ook ’n afbeelding tussen die vrye-deeltjie en wisselwerkende toestande waarbinne die Jastrow-Slater struktuur van die komposiete-fermion proefgolffunksies op ’n natuurlike wyse na vore kom. Verder werp ons formalisme nuwe lig op kwessies binne die standaard heuristiese konstruksie, veral met betrekking tot die oorsprong van die effektiewe magneetveld en die rol van ho¨er effektiewe Landau vlakke. Ons lewer ook uitspraak oor die vraagstuk van die oorvleueling van ongeprojekteerde komposiete-fermion golffunksies met die laagste Landau vlak van die vrye-deeltjie Landau probleem.
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Wynen, Jan-Lukas [Verfasser]. "Strongly interacting few-body systems from lattice stochastic methods / Jan-Lukas Wynen." Bonn : Universitäts- und Landesbibliothek Bonn, 2020. http://d-nb.info/1219140198/34.
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Mikelsons, Karlis. "Extensions of Numerical Methods for Strongly Correlated Electron Systems." University of Cincinnati / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1256909270.
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Van, Vlack Cole. "Time dependent complex scaling: Quantum dynamics in strongly perturbed systems." Thesis, University of Ottawa (Canada), 2008. http://hdl.handle.net/10393/28032.
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We have begun development of a tool for investigating the bound state dynamics of single electron systems in intense fields. This was done by implementing the method of uniform complex scaling in a 1D test system in two different ways and have shown that the use of the "c-norm" in non-Hermitian quantum mechanics can fail for time dependent simulations. We have developed the method of complex backscaling which transforms the wavefunction from the complex scaled space back into real space and have shown that it is more robust than the "c-norm" and predicts the correct ionization when compared to simulations done in real space. We have also begun using the complex scaling method in a 2D NZ model but it seems that the nature of the potential requires a more difficult type of scaling which causes problems within the calculations.
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Saelen, Lene. "Quantum control of strongly coupled dynamics in few component systems." Paris 6, 2009. http://www.theses.fr/2009PA066768.
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Ce travail concerne l’étude théorique et la modélisation de la dynamique du nuage électronique de systèmes quantiques simples ou modèles soumis à une perturbation extérieure dépendante du temps, dans des échelles de temps allant de la picoseconde à l’attoseconde. Les systèmes étudiés vont de molécules diatomiques ionisées par impact d’ions multichargés rapides à des systèmes mésoscopiques, de type boîte quantique moléculaire ou anneau quantique, en présence d’un champ électromagnétique dépendant du temps. La ligne directrice de ce travail a consisté à résoudre dans ces différents contextes l’équation de Schrödinger dépendante du temps par des méthodes non perturbatives totalement numériques. La thèse comporte neuf chapitres, les cinq premiers présentant les caractéristiques principales des systèmes considérés et les méthodes numériques utilisées et codées informatiquement pour réaliser les « expériences numériques » de modélisation. Le sixième concerne la description des algorithmes développés pour le contrôle de transitions "état-à-état" par l’optimisation (en fréquence, durée et intensité) de pulses électromagnétiques complexes auxquels sont soumis les systèmes quantiques mésoscopiques considérés. Sont présentés ensuite les résultats obtenus concernant (i) la stabilisation de molécules diatomiques sans électron par des champs électromagnétiques ultra-intenses, (ii) le contrôle d’une transition électronique vers un état de charge localisée dans un système de boîtes quantiques à deux électrons fortement corrélés par des pulses optimisés ainsi que (iii) l’étude de la décohérence en spin de ce derniers systèmes. Dans le cas des anneaux quantiques, un travail de synthèse de nos précédents travaux est également présenté pour démontrer la possibilité de construire un ensemble complet d’opérations sur des qubits (codés par le spin total et le moment angulaire total) dans la perspective de la réalisation d’ordinateurs quantiques. Finalement, la thèse s’achève par la présentation de nos calculs de sections efficaces différentielles d’ionisation de la molécule de dihydrogène par impact d’ions multichargés, notre travail ayant particulièrement porté sur l’analyse détaillée des effets d’interférences observées récemment expérimentalement
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Pietikäinen, I. (Iivari). "Strong radiation-matter interaction in a driven superconducting quantum system." Doctoral thesis, Oulun yliopisto, 2019. http://urn.fi/urn:isbn:9789526222479.
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Abstract In this thesis we study the interaction between radiation and matter using superconducting circuits that behave analogously with the conventional photon-atom interaction in quantum optics. The research is done with a system consisting of a waveguide resonator (radiation) strongly coupled to a transmon device (matter). We focus on the phenomena caused by strong coupling between the radiation and matter, and by driving the resonator to higher excited states with a strong monochromatic radiation. These have been studied little in the traditional radiation-matter systems. Increasing the strength of the monochromatic radiation drive, the dynamics of the system experiences a transition from the quantum to the classical regime. Also, the free-particle states of the transmon start being populated. In the weak driving limit, the transmon can be regarded as a two-state system. As a consequence, the resonator-transmon system is conventionally discussed in terms of the linear Jaynes–Cummings model. However, for strong coupling the Bloch–Siegert shift, caused by the terms neglected in the Jaynes–Cummings model, is strong and the Jaynes–Cummings model is insufficient for describing the dynamics of the system. We study the effects caused by strong coupling and the excitation of the higher transmon states instigated by the driving of the resonator. With reflection spectroscopy, we measure the absorption spectrum of the system and compare this with the spectrum calculated numerically using the Floquet–Born–Markov approach. We find that, in the region of the quantum-to-classical transition, the two-state approximation for the transmon is insufficient and the higher transmon states are necessary for accurate simulations. By calculating the average resonator occupation, we compare different numerical models: the Lindblad master equation, the Floquet–Born–Markov, and the semiclassical model. Coupling a transmon to a resonator shifts the energy levels of the resonator. This shift in the energy levels prevents the higher resonator states from being populated if the system is weakly driven with a frequency that is near the resonance frequency of the resonator. We simulate this photon blockade numerically and show that the blockade is substantially different for the two-state and multistate transmon approximationsOriginal papers Original papers are not included in the electronic version of the dissertation. Pietikäinen, I., Danilin, S., Kumar, K. S., Vepsäläinen, A., Golubev, D. S., Tuorila, J., & Paraoanu, G. S. (2017). Observation of the Bloch-Siegert shift in a driven quantum-to-classical transition. Physical Review B, 96(2). https://doi.org/10.1103/PhysRevB.96.020501 http://jultika.oulu.fi/Record/nbnfi-fe201803073899 Pietikäinen, I., Danilin, S., Kumar, K. S., Tuorila, J., & Paraoanu, G. S. (2018). Multilevel Effects in a Driven Generalized Rabi Model. Journal of Low Temperature Physics, 191(5–6), 354–364. https://doi.org/10.1007/s10909-018-1857-8 http://jultika.oulu.fi/Record/nbnfi-fe2018061325770 Pietikäinen, I., Tuorila, J., Golubev, D. S., & Paraoanu, G. S. (2019) Quantum-to-classical transition in the driven-dissipative Josephson pendulum coupled to a resonator, Manuscript. https://arxiv.org/abs/1901.05655
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Vilardi, Demetrio [Verfasser], and Walter [Akademischer Betreuer] Metzner. "Functional renormalization group for strongly interacting Fermi systems / Demetrio Vilardi ; Betreuer: Walter Metzner." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2019. http://d-nb.info/1183678509/34.
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Wendt, Kyle Andrew. "Advances in the Application of the Similarity Renormalization Group to Strongly Interacting Systems." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1375205117.
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Rau, Sebastian [Verfasser]. "Optimal Control of interacting Quantum Particle Systems / Sebastian Rau." München : Verlag Dr. Hut, 2013. http://d-nb.info/1042308470/34.
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Kerner, Joachim Friedrich. "Interacting many-particle systems on general compact quantum graphs." Thesis, University of London, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603454.
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In this thesis, we discuss many-particle systems on general compact quantum graphs. The results cover systems of distinguishable particles as well as systems of bosons or fermions. The main focus lies on the introduction of many-particle interactions in order to establish a useful model regarding many-particle quantum chaos 811d onc-dimensional Bose-Einstein condensation (BEC). Using suitable quadratic forms, we will characterise self-adjoint realisations of the two- and many-particle Laplacian which incorporate two different types of interactions, i.e. singular interactions localised at the vertices of the graph and contact interactions which are also present along the edges. In that context, we will establish regularity results in order to characteristic the domains of the self-adjoint realisations explicitly. We will also discuss spectral properties of the constructed operators by establishing discreteness of their spectra and Weyl laws for the corresponding eigenvalue counts. Finally, based on the introduced models of interacting particles, we discuss BoseEinstein condensation on general quantum graphs. We will distinguish between systems of bosons for which BEC occurs and such for which no BEC is present at any finite temperature. As a final result, we prove that no Bose-Einstein condensation occurs (in the sense of phase transitions) in a system of bosons interacting via repulsive hard-core interactions.
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Kovacs, E., and Z. Gulacsi. "Exact ground states for quasi 1D systems with hubbard interaction." Thesis, Sumy State University, 2011. http://essuir.sumdu.edu.ua/handle/123456789/20658.
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Using a positive semidefinite operator technique we deduced exact ground states for a modified diamond chain described by a non-integrable Hubbard model with on-site repulsion. Our results are valid for arbitrary length of the chain and strength of the Hubbard interaction. For the analyzed quasi 1D chain structure we found that two flat bands are present in the bare band structure of the system, both for zero and for a fixed value of magnetic field. We obtained ground states of nonmagnetic and ferromagnetic insulator type and studied their physical properties.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/20658
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Raum, Peter Thomas. "Exact Diagonalization Studies of Strongly Correlated Systems." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/96440.
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In this dissertation, we use exact diagonalization to study a few strongly correlated systems, ranging from the Fermi-Hubbard model to the fractional quantum Hall effect (FQHE). The discussion starts with an overview of strongly correlated systems and what is meant by strongly correlated. Then, we extend cluster perturbation theory (CPT), an economic method for computing the momentum and energy resolved Green's function for Hubbard models to higher order correlation functions, specifically the spin susceptibility. We benchmark our results for the one-dimensional Fermi-Hubbard model at half-filling. In addition we study the FQHE at fillings $nu = 5/2$ for fermions and $nu = 1/2$ for bosons. For the $nu = 5/2$ system we investigate a two-body model that effectively captures the three-body model that generates the Moore-Read Pfaffian state. The Moore-Read Pfaffian wave function pairs composite fermions and is believed to cause the FQHE at $nu = 5/2$. For the $nu = 1/2$ system we estimate the entropy needed to observe Laughlin correlations with cold atoms via an ansatz partition function. We find entropies achieved with conventional cooling techniques are adequate.Doctor of Philosophy
Strongly correlated quantum many-body physics is a rich field that hosts a variety of exotic phenomena. By quantum many-body we mean physics that is concerned with the behavior of interacting particles, such as electrons, where the quantum behavior cannot be ignored. By strongly correlated, we mean when the interactions between particles are sufficiently strong such that they cannot be treated as a small perturbation. In contrast to weakly correlated systems, strongly correlated systems are much more difficult to solve. That is because methods that reduce the many-body problem to a single independent body problem do not work well. In this dissertation we use exact diagonalization, a method to computationally solve quantum many-body systems, to study two strongly correlated systems: the Hubbard model and the fractional quantum Hall effect.The Hubbard model captures the physics of many interesting materials and is the standard toy model. Originally developed with magnetic properties in mind, it has been extended to study superconductivity, topological phases, cold atoms, and much more. The fractional quantum Hall effect is a novel phase of matter that hosts exotic excitations, some of which may have applications to quantum computing.
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Piga, Angelo. "Entanglement and Bell correlations in strongly correlated many-body quantum systems." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/669100.
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During the past two decades, thanks to the mutual fertilization of the research in quantum information and condensed matter, new approaches based on purely quantum features without any classical analog turned out to be very useful in the characterization of many-body quantum systems (MBQS). A peculiar role is obviously played by the study of purely quantum correlations, manifesting in the “spooky” properties of entanglement and nonlocality (or Bell correlations), which ultimately discriminate classical from quantum regimes. It is, in fact, such kind of correlations that give rise to the plethora of intriguing emergent behaviors of MBQS, which cannot be reduced to a mere sum of the behaviors of individual components, the most important example being the quantum phase transitions. However, despite being indeed closely related concepts, entanglement and nonlocality are actually two different resources.
With regard to the entanglement, we will use it to characterize several instances of MBQS, to exactly locate and characterize quantum phase transitions in spin-lattices and interacting fermionic systems, to classify different gapped quantum phases according to their topological features and to provide a purely quantum signature of chaos in dynamical systems.
Our approach will be mainly numerical and for simulating the ground states of several one-dimensional lattice systems we draw heavily on the celebrated “density matrix renormalization group” (DMRG) algorithm in the “matrix product state” (MPS) ansatz. A MPS is a one-dimensional tensor network (TN) representation for quantum states and occupies a pivotal position in what we have gained in thinking MBQS from an entanglement perspective. In fact, the success of TNs states mainly relies on their fulfillment, by construction, of the so called “entanglement area law”. This is a feature shared by the ground states of gapped Hamiltonians with short-range interactions among the components and consists of a sub-extensive entanglement entropy, which grows only with the surface of the bipartition. This property translates in a reduced complexity of such systems, allowing affordable simulations, with an exponential reduction of computational costs. Besides the use of already existing TN-based algorithms, an effort will be done to develop a new one suitable for high-dimensional lattices.
While many useful results are available for the entanglement in many different contexts, less is known about the role of nonlocality. Formally, a state of a multi-party system is defined nonlocal if its correlations violate some “Bell inequality” (BI). The derivation of the BIs for systems consisting of many parties is a formidable task and only recently, a class of them, relevant for nontrivial states, has been proposed. In an important chapter of the thesis, we apply these BIs to fully characterize the phase transition of a long-range ferromagnetic Ising model, doing a comparison with entanglement-based results and then making one of the first efforts in the study of MBQS from a nonlocality perspective.Durante las dos últimas décadas, gracias al enriquecimiento mutuo entre las investigaciones en información cuántica y materia condensada, se han desarrollado nuevos enfoques que han resultado muy útiles en la caracterización de los sistemas cuánticos de muchos cuerpos (SCMC), basados en características puramente cuánticas sin ningún análogo clásico. El estudio de las correlaciones puramente cuánticas juega obviamente un papel fundamental. Estas correlaciones se manifiestan en las propiedades del entrelazamiento cuántico (“entanglement”) y no-localidad (o correlaciones de Bell), que en última instancia discriminan los regímenes clásicos de los regímenes cuánticos. Este tipo de correlaciones son, de hecho, las que dan lugar a la plétora de comportamientos emergentes enigmáticos de los SCMC, que no pueden reducirse a una mera suma de los comportamientos de los componentes individuales, siendo el ejemplo más importante siendo las transiciones de fase cuánticas (TFC). Sin embargo, a pesar de ser conceptos estrechamente relacionados, el entrelazamiento y la no-localidad son en realidad dos recursos diferentes. Con respecto al entrelazamiento, lo utilizaremos para caracterizar varios ejemplos de SCMC, para localizar y caracterizar exactamente las TFC en retículos de espines y de sistemas de fermiones interactuantes, para clasificar las diferentes fases cuánticas de acuerdo con su topología y para proporcionar una señal puramente cuántica del caos en los sistemas dinámicos. Nuestro enfoque será principalmente numérico y para simular los estados fundamentales de varios sistemas unidimensionales nos basamos en gran medida en el célebre algoritmo “density matrix renormalization group” (DMRG), formulado en el ansatz de los “matrix product states” (MPS). Un MPS es un “retículos de tensores” (“tensor networks”, TN) unidimensional que representa estados cuánticos y ocupa una posición central entre los mayores logros obtenidos al estudiar los SCMC desde la perspectiva del entrelazamiento cuántico. De hecho, el éxito de los TN depende principalmente de su cumplimiento, por construcción, de una “ley del área” (“area-law”) de la entropía de entrelazamiento. Esta es una característica compartida por los estados fundamentales de los Hamiltonianos con interacciones de corto alcance entre los componentes del sistema y con una brecha (“gap”) entre el estado fundamental y los niveles excitados, que consiste en una entropía de entrelazamiento subextensiva, que crece sólo con la superficie de la bipartición. Esta propiedad se traduce en una menor complejidad de dichos sistemas, permitiendo simulaciones asequibles, con una reducción exponencial de los costes computacionales. Además del uso de los algoritmos ya existentes basados en TN, se desarrollará uno nuevo adecuado para sistemas en dimensiones altas. Si bien se dispone de muchos resultados útiles para el entrelazamiento en muchos contextos diferentes, se sabe menos sobre el papel jugado por la no-localidad. Formalmente, un estado de un sistema compuesto de muchas partes, se define como no-local si sus correlaciones violan alguna “desigualdad de Bell” (“Bell inequality”, BI). La derivación de dichas desigualdades para sistemas compuestos de muchas partes es un reto y sólo recientemente se ha propuesto una clase de ellas, relevante para estados no triviales. En un capítulo importante de la tesis, aplicamos estas BIs para caracterizar completamente la transición de fase de un modelo de Ising ferromagnético con interacciones de largo alcance, haciendo una comparación con los resultados basados en el entrelazamiento y luego haciendo uno de los primeros esfuerzos en el estudio de los SCMC desde una perspectiva de la no-localidad.
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Saberi, Hamed. "Matrix-product states for strongly correlated systems and quantum information processing." Diss., lmu, 2009. http://nbn-resolving.de/urn:nbn:de:bvb:19-97552.
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Chudnovsky, Victor 1974. "Strongly coupled systems : from quantum antiferromagnets to unified models for superconductors." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/29895.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2002.Includes bibliographical references (p. 109-118) and index.
I discuss the significance of the antiferromagnetic Heisenberg model (AFHM) in both high-energy and condensed-matter physics, and proceed to describe an efficient cluster algorithm used to simulate the AFHM. This is one of two algorithms with which my collaborators and I were able to obtain numerical results that definitively confirm that chiral perturbation theory, corrected for cutoff effects in the AFHM, leads to a correct field-theoretical description of the low-temperature behavior of the spin correlation length in various spin representations S. Using a finite-size-scaling technique, we explored correlation lengths of up to 105 lattice spacings for spins S=1 and 5/2. We show how the recent prediction of cutoff effects by P. Hasenfratz is approached for moderate correlation lengths, and smoothly connects with other approaches to modeling the AFHM at smaller correlation lengths. I also simulate and discuss classical antiferromagnetic systems with simultaneous SO(M) and SO(N) symmetries, which have been proposed as models for magnets in external fields and for electronic and color superconductors. After detailing the algorithms which were employed, I present results for the various observables which confirm the existence of the expected ordered and disordered phases. I obtain a preliminary phase diagram from these systems, from which the location of an expected bicritical point may be estimated. This is a necessary first step in determining whether the point exhibits a dynamically-generated enhanced symmetry, a possibility first suggested by Wiese and Chandrasekharan but not fully resolved in three dimensions.
by Victor Chudnovsky.
Ph.D.
50
Robinson, Neil Joe. "Pairing, paramagnetism and prethermalization in strongly correlated low-dimensional quantum systems." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:167d164c-e318-49b3-83ea-69b54ec531e0.
Full textAbstract:
Quasi-one-dimensional quantum models are ideal for theoretically exploring the physical phenomena associated with strong correlations. In this thesis we study three examples where strong correlations play an important role in the static or dynamic properties of the system. Firstly, we examine the behaviour of a doped fermionic two-leg ladder in which umklapp interactions are present. Such interactions arise at special band fillings and can be induced by the formation of charge density wave order in an array of two-leg ladders with long-range (three-dimensional) interactions. For the umklapp which arises from the half-filling of one of the bands, we show that the low-energy theory has a number of phases, including a strong coupling regime in which the dominant fluctuations are superconducting in nature. These superconducting fluctuations carry a finite wave vector – they are the one-dimensional analogue of Fulde-Ferrell-Larkin-Ovchinnikov superconductivity. In a second example, we consider a quantum spin model which captures the essential one-dimensional physics of CoNb2O6, a quasi-one-dimensional Ising ferromagnet. Motivated by high-resolution inelastic neutron scattering experiments, we calculate the dynamical structure in the paramagnetic phase and show that a small misalignment of the transverse field can lead to quasi-particle breakdown – a surprising broadening in the single particle mode observed in experiment. Finally, we study the out-of-equilibrium dynamics of a model with tuneable integrability breaking. When integrability is broken by the presence of weak interactions, we show that the system relaxes to a non-thermal state on intermediate time scales, the so-called “prethermalization plateau”. We describe the approximately stationary behaviour in this regime by constructing a generalised Gibbs ensemble with charges deformed to leading order in perturbation theory. Expectation values of these charges are time-independent, but interestingly the charges do not commute with the Hamiltonian to leading order in perturbation theory. Increasing the strength of the integrability breaking interactions leads to behaviour compatible with thermalisation. In each case we use a combination of perturbative analytical calculations and non-perturbative numerical computations to study the problem at hand.