Articles de revues : « Low Dimensional Quantum Spin Systems »

1

Dillenschneider, Raoul, Jung Hoon Kim et Jung Hoon Han. « Vector Chiral States in Low-Dimensional Quantum-Spin Systems ». Journal of the Korean Physical Society 53, n^o 2 (14 août 2008) : 732–36. http://dx.doi.org/10.3938/jkps.53.732.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

2

Wolf, B., S. Zherlitsyn, U. Löw, B. Lüthi, V. Pashchenko et M. Lang. « Low-dimensional quantum spin systems in pulsed magnetic fields ». Physica B : Condensed Matter 346-347 (avril 2004) : 19–26. http://dx.doi.org/10.1016/j.physb.2004.01.013.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

3

Lemmens, P., G. Güntherodt et C. Gros. « Magnetic light scattering in low-dimensional quantum spin systems ». Physics Reports 375, n^o 1 (février 2003) : 1–103. http://dx.doi.org/10.1016/s0370-1573(02)00321-6.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

4

Lima, Leonardo S. « Entanglement Negativity and Concurrence in Some Low-Dimensional Spin Systems ». Entropy 24, n^o 11 (10 novembre 2022) : 1629. http://dx.doi.org/10.3390/e24111629.

Texte intégral

Résumé :

The influence of magnon bands on entanglement in the antiferromagnetic XXZ model on a triangular lattice, which models the bilayer structure consisting of an antiferromagnetic insulator and normal metal, is investigated. This effect was studied in ferromagnetic as well as antiferromagnetic triangular lattices. Quantum entanglement measures given by the entanglement negativity have been studied, where a magnon current is induced in the antiferromagnet due to interfacial exchange coupling between localized spins in the antiferromagnet and itinerant electrons in a normal metal. Moreover, quantum correlations in other frustrated models, namely the metal-insulation antiferromagnetic bilayer model and the Heisenberg model with biquadratic and bicubic interactions, are analyzed.

Styles APA, Harvard, Vancouver, ISO, etc.

5

HORVATIĆ, M., et C. BERTHIER. « HIGH FIELD NMR IN STRONGLY CORRELATED LOW-DIMENSIONAL FERMIONIC SYSTEMS ». International Journal of Modern Physics B 16, n^o 20n22 (30 août 2002) : 3265–70. http://dx.doi.org/10.1142/s0217979202014127.

Texte intégral

Résumé :

We review some recent NMR results obtained in Grenoble High Magnetic Field Laboratory on magnetic field induced phenomena in strongly correlated low-dimensional fermionic systems: i) magnetic field dependence of the soliton lattice in the IC phase of the spin-Peierls system CuGeO3, ii) NMR study of the complete H-T phase diagram of the organo-metallic spin ladder Cu2(C5H12N2)2Cl4, and iii) the first "standard" NMR measurements (i.e., without optical pumping) on 2D electrons in Quantum wells, providing a detailed description of the fractional quantum Hall effect state at ν = 1/2 with the first determination of the corresponding effective polarization mass of composite fermions. Latest study of the ν = 2/3 state revealed, among other features, an unexpected phase transition.

Styles APA, Harvard, Vancouver, ISO, etc.

6

Ercolessi, Elisa. « ONE AND QUASI-ONE DIMENSIONAL SPIN SYSTEMS ». Modern Physics Letters A 18, n^o 33n35 (20 novembre 2003) : 2329–36. http://dx.doi.org/10.1142/s0217732303012544.

Texte intégral

Résumé :

Quantum spin models represent one of the most studied examples of application of low-dimensional field theories to condensed matter systems. In this paper we will review some chapters of this hystory, that dates back to the early '80, when Haldane put forward his by now famous conjecture on antiferromagnetic spin chains, and reaches the present days, with the most advanced applications of integrable models and conformal field theory.

Styles APA, Harvard, Vancouver, ISO, etc.

7

Saha-Dasgupta, Tanusri. « The Fascinating World of Low-Dimensional Quantum Spin Systems : Ab Initio Modeling ». Molecules 26, n^o 6 (10 mars 2021) : 1522. http://dx.doi.org/10.3390/molecules26061522.

Texte intégral

Résumé :

In recent times, ab initio density functional theory has emerged as a powerful tool for making the connection between models and materials. Insulating transition metal oxides with a small spin forms a fascinating class of strongly correlated systems that exhibit spin-gap states, spin–charge separation, quantum criticality, superconductivity, etc. The coupling between spin, charge, and orbital degrees of freedom makes the chemical insights equally important to the strong correlation effects. In this review, we establish the usefulness of ab initio tools within the framework of the N-th order muffin orbital (NMTO)-downfolding technique in the identification of a spin model of insulating oxides with small spins. The applicability of the method has been demonstrated by drawing on examples from a large number of cases from the cuprate, vanadate, and nickelate families. The method was found to be efficient in terms of the characterization of underlying spin models that account for the measured magnetic data and provide predictions for future experiments.

Styles APA, Harvard, Vancouver, ISO, etc.

8

Ohta, H., S. Okubo, S. Kimura, T. Sakurai, S. Takeda, T. Tanaka, H. Kikuchi et H. Nagasawa. « Submillimeter-wave ESR measurements of low-dimensional quantum spin systems ». Applied Magnetic Resonance 18, n^o 4 (avril 2000) : 469–74. http://dx.doi.org/10.1007/bf03162293.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

9

Wang, Dong-Sheng. « Classes of topological qubits from low-dimensional quantum spin systems ». Annals of Physics 412 (janvier 2020) : 168015. http://dx.doi.org/10.1016/j.aop.2019.168015.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

10

WOLF, B., S. ZHERLITSYN, S. SCHMIDT, B. LÜTHI et M. LANG. « PULSE-FIELD EXPERIMENTS ON THE SPIN-LATTICE INTERACTION IN LOW-DIMENSIONAL SPIN SYSTEMS ». International Journal of Modern Physics B 16, n^o 20n22 (30 août 2002) : 3369–72. http://dx.doi.org/10.1142/s0217979202014449.

Texte intégral

Résumé :

Low-dimensional spin systems reveal new and unexpected physical phenomena such as distinct plateaus in the magnetization as a function of magnetic field. In this paper we present ultrasonic measurements for the quasi-two-dimensional spin system SrCu2(BO3)2 in magnetic fields up to 50 T. From this technique we obtained detailed information about the spin state, the magnetic excitations and their interaction with phonons. The dimerized quantum-spin system SrCu2(BO3)2 exhibits plateaus in the magnetization and shows surprisingly strong magneto-elastic effects as a function of temperature and magnetic field. The pronounced elastic anomalies indicate a resonant interaction between the sound wave and the magnetic excitations.

Styles APA, Harvard, Vancouver, ISO, etc.

11

Ding, L. J., K. L. Yao et H. H. Fu. « Spin-Peierls transition in low-dimensional quantum spin systems : a Green’s function approach ». Physical Chemistry Chemical Physics 11, n^o 48 (2009) : 11415. http://dx.doi.org/10.1039/b913654a.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

12

LHUILLIER, C., B. BERNU et G. MISGUICH. « GEOMETRICALLY FRUSTRATED QUANTUM ANTIFERROMAGNETS AND SPIN-LIQUIDS ». International Journal of Modern Physics B 13, n^o 05n06 (10 mars 1999) : 687–95. http://dx.doi.org/10.1142/s0217979299000588.

Texte intégral

Résumé :

We briefly review experimental and theoretical results related to the problem of long range magnetic order in geometrically frustrated 2-dimensional quantum antiferromagnets. We show that 2-dimensional He3 at low coverage is a good candidate as a Spin-Liquid. We underline that sophisticated numerical studies of the spectra of such systems point at least to two different kinds of Spin-Liquids.

Styles APA, Harvard, Vancouver, ISO, etc.

13

Alexander, Rafael N., Glen Evenbly et Israel Klich. « Exact holographic tensor networks for the Motzkin spin chain ». Quantum 5 (21 septembre 2021) : 546. http://dx.doi.org/10.22331/q-2021-09-21-546.

Texte intégral

Résumé :

The study of low-dimensional quantum systems has proven to be a particularly fertile field for discovering novel types of quantum matter. When studied numerically, low-energy states of low-dimensional quantum systems are often approximated via a tensor-network description. The tensor network's utility in studying short range correlated states in 1D have been thoroughly investigated, with numerous examples where the treatment is essentially exact. Yet, despite the large number of works investigating these networks and their relations to physical models, examples of exact correspondence between the ground state of a quantum critical system and an appropriate scale-invariant tensor network have eluded us so far. Here we show that the features of the quantum-critical Motzkin model can be faithfully captured by an analytic tensor network that exactly represents the ground state of the physical Hamiltonian. In particular, our network offers a two-dimensional representation of this state by a correspondence between walks and a type of tiling of a square lattice. We discuss connections to renormalization and holography.

Styles APA, Harvard, Vancouver, ISO, etc.

14

Tomic, S., T. Vuletic, M. Pinteric et B. Korin-Hamzic. « Modalities of self-organized charge response in low dimensional systems ». Journal de Physique IV 12, n^o 9 (novembre 2002) : 211–14. http://dx.doi.org/10.1051/jp4:20020397.

Texte intégral

Résumé :

We present modalities of self-organized charge response in low dimensional systems, like diverse organic and quantum spin systems, studied by the low-frequency (10 mHz – 1 MHz) dielectric spectroscopy. Density wave structures with the order of commensurability N = 4 can be recognized as phasons in a random impurity potential, whereas those with N = 3 can be viewed as topological defects like charge domain wall pairs in the background domain structure.

Styles APA, Harvard, Vancouver, ISO, etc.

15

BRAUN, HANS-BENJAMIN, et DANIEL LOSS. « CHIRALITY CORRELATION OF SPIN SOLITONS : BLOCH WALLS, SPIN-½ SOLITONS AND HOLES IN A 2D ANTIFERROMAGNETIC BACKGROUND ». International Journal of Modern Physics B 10, n^o 02 (20 janvier 1996) : 219–34. http://dx.doi.org/10.1142/s021797929600009x.

Texte intégral

Résumé :

We consider the quantum dynamics of spin solitons in a variety of low-dimensional magnetic systems in the semiclassical and the extreme quantum limit. Introducing the concept of chirality of the soliton we derive the dispersion of spin solitons moving through a periodic pinning potential and show that for half-odd integer spin the topological part of the Berry phase induces a halving of the Brillouin zone as well as chirality correlations between subsequent band minima. We demonstrate that these chirality and spin parity effects are universal by considering quasi-one-dimensional ferromagnets and antiferromagnets with local anisotropies and large spins, as well as spin-½ ferromagnetic and antiferromagnetic Heisenberg chains in the Ising limit. For large spin systems, the tunneling rate between states of opposite chiralities is derived and shown to provide a novel scenario for macroscopic quantum phenomena. The results are extended to solitons moving as holes in a two-dimensional antiferromagnetic background, leading to a hole spectrum which is in remarkable agreement with recent ARPES measurements on high-Tc compounds.

Styles APA, Harvard, Vancouver, ISO, etc.

16

ANGELUCCI, ANTIMO, et GIANCARLO JUG. « NOVEL PATH INTEGRAL APPROACH TO EFFECTIVE FIELD THEORIES FOR D-DIMENSIONAL QUANTUM SPIN SYSTEMS ». International Journal of Modern Physics B 03, n^o 07 (juillet 1989) : 1069–83. http://dx.doi.org/10.1142/s0217979289000737.

Texte intégral

Résumé :

We present a novel path integral formulation for the effective field theory describing d-dimensional quantum spin models. The new approach avoids the coherent states representation, but at very low temperatures reproduces all known results obtained with the latter technique for describing excitations of the Neél state. The possibility of exploring higher-temperature, unbroken-symmetry state excitations (such as those appropriate for the quantum spin-liquid state) within this method is illustrated.

Styles APA, Harvard, Vancouver, ISO, etc.

17

Kamieniarz, G., G. Musial, L. Dębski, M. Bieliński et R. Dekeyser. « Quantum Effects and Critical Behavior in Low-Dimensional Spin-1/2 Systems ». Acta Physica Polonica A 92, n^o 2 (août 1997) : 445–47. http://dx.doi.org/10.12693/aphyspola.92.445.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

18

Wei, Di S., Toeno van der Sar, Seung Hwan Lee, Kenji Watanabe, Takashi Taniguchi, Bertrand I. Halperin et Amir Yacoby. « Electrical generation and detection of spin waves in a quantum Hall ferromagnet ». Science 362, n^o 6411 (11 octobre 2018) : 229–33. http://dx.doi.org/10.1126/science.aar4061.

Texte intégral

Résumé :

Spin waves are collective excitations of magnetic systems. An attractive setting for studying long-lived spin-wave physics is the quantum Hall (QH) ferromagnet, which forms spontaneously in clean two-dimensional electron systems at low temperature and in a perpendicular magnetic field. We used out-of-equilibrium occupation of QH edge channels in graphene to excite and detect spin waves in magnetically ordered QH states. Our experiments provide direct evidence for long-distance spin-wave propagation through different ferromagnetic phases in the N = 0 Landau level, as well as across the insulating canted antiferromagnetic phase. Our results will enable experimental investigation of the fundamental magnetic properties of these exotic two-dimensional electron systems.

Styles APA, Harvard, Vancouver, ISO, etc.

19

Shamim, Saquib, Wouter Beugeling, Jan Böttcher, Pragya Shekhar, Andreas Budewitz, Philipp Leubner, Lukas Lunczer, Ewelina M. Hankiewicz, Hartmut Buhmann et Laurens W. Molenkamp. « Emergent quantum Hall effects below 50 mT in a two-dimensional topological insulator ». Science Advances 6, n^o 26 (juin 2020) : eaba4625. http://dx.doi.org/10.1126/sciadv.aba4625.

Texte intégral

Résumé :

The realization of the quantum spin Hall effect in HgTe quantum wells has led to the development of topological materials, which, in combination with magnetism and superconductivity, are predicted to host chiral Majorana fermions. However, the large magnetization in conventional quantum anomalous Hall systems makes it challenging to induce superconductivity. Here, we report two different emergent quantum Hall effects in (Hg,Mn)Te quantum wells. First, a previously unidentified quantum Hall state emerges from the quantum spin Hall state at an exceptionally low magnetic field of ~50 mT. Second, tuning toward the bulk p-regime, we resolve quantum Hall plateaus at fields as low as 20 to 30 mT, where transport is dominated by a van Hove singularity in the valence band. These emergent quantum Hall phenomena rely critically on the topological band structure of HgTe, and their occurrence at very low fields makes them an ideal candidate for realizing chiral Majorana fermions.

Styles APA, Harvard, Vancouver, ISO, etc.

20

Clark, Lucy, et Aly H. Abdeldaim. « Quantum Spin Liquids from a Materials Perspective ». Annual Review of Materials Research 51, n^o 1 (26 juillet 2021) : 495–519. http://dx.doi.org/10.1146/annurev-matsci-080819-011453.

Texte intégral

Résumé :

Quantum spin liquids are unique quantum states of matter predicted to arise in low-dimensional, frustrated, and quantum magnetic systems. Compared with conventional ferromagnetic and antiferromagnetic states, quantum spin liquids are expected to display a variety of novel and exotic properties, making their realization in materials a highly appealing prospect. While an unambiguous realization of this long-sought-after state remains elusive, a growing number of materials candidates show promise in revealing the properties of quantum spin liquids. In this review, we present some of the key challenges and current opportunities in the synthesis, characterization, and understanding of quantum spin liquids from the perspective of the broad and interdisciplinary field of materials research.

Styles APA, Harvard, Vancouver, ISO, etc.

21

Glatz, A., et T. Nattermann. « Quantum phase slips and thermal fluctuations in one-dimensional disordered density waves ». Journal de Physique IV 12, n^o 9 (novembre 2002) : 123–26. http://dx.doi.org/10.1051/jp4:20020376.

Texte intégral

Résumé :

The low temperature phase diagram of 1D disordered quantum systems like charge or spin density waves, superfluids, and related systems is considered by a full finite T renormalization group approach for the first time. At zero temperature the consideration of quantum phase slips leads to a new scenario for the unpinning (delocalization) transition. In the strong pinning limit the model is solved exactly. At finite T a rich crossover diagram with various scaling regions is found which reflects the zero temperature quantum critical behavior.

Styles APA, Harvard, Vancouver, ISO, etc.

22

Ohta, Hitoshi, Susumu Okubo, Yuji Inagaki, Zenji Hiroi et Hikomitsu Kikuchi. « Recent high field ESR studies of low-dimensional quantum spin systems in Kobe ». Physica B : Condensed Matter 346-347 (avril 2004) : 38–44. http://dx.doi.org/10.1016/j.physb.2004.01.016.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

23

Rajashabala, S., et K. Navaneethakrishnan. « Pressure effects on the spin–orbit interactions in low-dimensional quantum well systems ». Physica E : Low-dimensional Systems and Nanostructures 40, n^o 4 (février 2008) : 843–48. http://dx.doi.org/10.1016/j.physe.2007.10.104.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

24

Richert, Jean, et Otfried Gühne. « Low energy properties of even-leggedd-dimensional quantum spin systems : a variational approach ». physica status solidi (b) 245, n^o 8 (août 2008) : 1552–62. http://dx.doi.org/10.1002/pssb.200743512.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

25

Wolf, B., S. Zherlitsyn, S. Schmidt et B. L�thi. « Low-Dimensional Quantum Spin Systems in Pulsed Magnetic Fields up to 50 T ». physica status solidi (a) 189, n^o 2 (février 2002) : 389–96. http://dx.doi.org/10.1002/1521-396x(200202)189:2<389 ::aid-pssa389>3.0.co;2-p.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

26

Kakurai, K., M. Nishi, K. Nakajima, K. Nukui, N. Aso, T. Kato, H. Tanaka et al. « Neutron scattering experiments on low-dimensional quantum spin systems—Spin excitations in KCuCl3 and SrCu2(BO3)2 ». Journal of Physics and Chemistry of Solids 62, n^o 1-2 (janvier 2001) : 141–47. http://dx.doi.org/10.1016/s0022-3697(00)00116-5.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

27

YOU, WEN-LONG, et WEN-LONG LU. « GROUND-STATE CORRELATION ENTROPY IN THE ONE- AND TWO-DIMENSIONAL XXZ MODEL ». International Journal of Modern Physics B 25, n^o 02 (20 janvier 2011) : 231–41. http://dx.doi.org/10.1142/s0217979211057815.

Texte intégral

Résumé :

In this paper, we study quantum phase transitions in both the one- (1D) and two-dimensional (2D) spin 1/2 XXZ models by a two-site correlation entropy. We show that the behavior of the correlation entropy is related to the ground-state symmetries and low-lying excitations of these systems. Therefore, the anomalies and minimum behaviors of the correlation entropy can signal the quantum phase transition points in the ground state of both models.

Styles APA, Harvard, Vancouver, ISO, etc.

28

Cheranovskii, Vladislav O., Viktor V. Slavin, Elena V. Ezerskaya, Andrei L. Tchougréeff et Richard Dronskowski. « Magnetic Properties of Quasi-One-Dimensional Crystals Formed by Graphene Nanoclusters and Embedded Atoms of the Transition Metals ». Crystals 9, n^o 5 (15 mai 2019) : 251. http://dx.doi.org/10.3390/cryst9050251.

Texte intégral

Résumé :

Using the density-matrix renormalization group method and quantum Monte Carlo simulation, we studied numerically the energy spectrum and thermodynamics of the quantum Heisenberg spin model for narrow graphene nanoribbons and their derivatives with periodically embedded heteroatoms. For several nanoribbon structures we found macroscopic ground state spin, gapless lowest excitation spectra and intermediate magnetization plateaus at low temperatures. We also studied the lowest energy states of frustrated systems formed by triangular graphitic clusters connected by bridged ions of transition metals. On the base of many-body perturbation theory and the exact diagonalization method, we showed the possibility of spin switching for this model due to the change the corresponding coupling parameters.

Styles APA, Harvard, Vancouver, ISO, etc.

29

KISHINE, JUN-ICHIRO, et KENJI YONEMITSU. « DIMENSIONAL CROSSOVERS AND PHASE TRANSITIONS IN STRONGLY CORRELATED LOW-DIMENSIONAL ELECTRON SYSTEMS : RENORMALIZATION-GROUP STUDY ». International Journal of Modern Physics B 16, n^o 05 (20 février 2002) : 711–71. http://dx.doi.org/10.1142/s0217979202009962.

Texte intégral

Résumé :

Based on the perturbative renormalization-group (PRG) approach, we have examined interplay or competition between one-particle (1P) and two-particle (2P) processes in strongly correlated low-dimensional electron systems. Throughout the article, we use the Grassmann functional integral approach, since it has an advantage that the 1P degrees of freedom are incorporated in an explicit manner. We mainly discuss an array of chains weakly-coupled via interchain one-particle hopping, where the constituent chains, if isolated, have a strong-coupling fixed point, such as the Mott-insulator, spin-gap-metal, or Anderson-insulator fixed point. In such cases, quantum fluctuations evolving toward the low-energy limit strongly suppress the interchain 1P coherence, and consequently a phase transition from the incoherent metallic (ICM) phase becomes possible. This kind of competition plays a key role to elucidate the interplay of correlation and dimensionality effects in real quasi-one-dimensional (Q1D) materials in nature. As examples, we take up spin-density-wave (SDW) phase transitions in dimerized quarter-filled Hubbard chains to elucidate the nature of the magnetic phase transitions in the Q1D organic conductors, (TMTTF)2X and (TMTSF)2X. Dimensional crossover problems in Q1D Hubbard ladders are also discussed to describe the pressure-induced superconductivity in the doped ladder systems. Interplay of randomness, electron correlation, and dimensionality effects in weakly-coupled half-filled Hubbard chains with weak quenched random potentials is also studied. We also discuss some 2D electron systems where the two-loop renormalization-group procedure is well defined and works.

Styles APA, Harvard, Vancouver, ISO, etc.

30

Zivieri, Roberto. « Absence of Spontaneous Spin Symmetry Breaking in 1D and 2D Quantum Ferromagnetic Systems with Bilinear and Biquadratic Exchange Interactions ». Symmetry 12, n^o 12 (11 décembre 2020) : 2061. http://dx.doi.org/10.3390/sym12122061.

Texte intégral

Résumé :

Some measurements have shown that the second-order exchange interaction is non-negligible in ferromagnetic compounds whose microscopic interactions are described by means of half-odd integer quantum spins. In these spin systems the ground state is either ferromagnetic or antiferromagnetic when the bilinear exchange interaction is dominant. Instead, in ferromagnetic systems characterized by bilinear and biquadratic exchange interactions of comparable magnitude, the energy minimum occurs when spins are in a canting ground-state. To this aim, a one-dimensional (1D) quantum spin chain and a two-dimensional (2D) lattice of quantum spins subjected to periodic boundary conditions are modeled via the generalized quantum Heisenberg Hamiltonian containing, in addition to the isotropic and short-range bilinear exchange interaction of the Heisenberg type, a second-order interaction, the isotropic and short-range biquadratic exchange interaction between nearest-neighbors quantum spins. For these 1D and 2D quantum systems a generalization of the Mermin–Wagner–Hohenberg theorem (also known as Mermin–Wagner–Berezinksii or Coleman theorem) is given. It is demonstrated, by means of quantum statistical arguments, based on Bogoliubov’s inequality, that, at any finite temperature, (1) there is absence of long-range order and that (2) the law governing the vanishing of the order parameter is the same as in the bilinear case for both 1D and 2D quantum ferromagnetic systems. The physical implications of the absence of a spontaneous spin symmetry breaking in 1D spin chains and 2D spin lattices modeled via a generalized quantum Heisenberg Hamiltonian are discussed.

Styles APA, Harvard, Vancouver, ISO, etc.

31

Cangas, R., et M. A. Hidalgo. « Influence of the Spin–Orbit Interaction on the Magnetotransport Properties of a Two-Dimensional Electron System ». SPIN 05, n^o 03 (septembre 2015) : 1530003. http://dx.doi.org/10.1142/s2010324715300030.

Texte intégral

Résumé :

In this paper, we review the contribution of the Rashba spin–orbit coupling to the magnetoconduction of a two-dimensional electron system (2DES) confined in an inversion layer under quantum Hall regime (low temperature and low defects and impurities). The study is based on a semi-classical model for the magnetoconductivities of the 2DES. This model reproduces the measurements of the Shubnikov-de Haas (SdH) oscillations obtained in systems confined in III–V heterostructures, and also the quantum Hall magnetoconductivity (magnetoresistivity). We also discuss the Rashba and Zeeman competition and its effect on the magnetoconductivity.

Styles APA, Harvard, Vancouver, ISO, etc.

32

NUSSINOV, ZOHAR, CRISTIAN D. BATISTA et EDUARDO FRADKIN. « INTERMEDIATE SYMMETRIES IN ELECTRONIC SYSTEMS : DIMENSIONAL REDUCTION, ORDER OUT OF DISORDER, DUALITIES, AND FRACTIONALIZATION ». International Journal of Modern Physics B 20, n^o 30n31 (20 décembre 2006) : 5239–49. http://dx.doi.org/10.1142/s0217979206036326.

Texte intégral

Résumé :

We discuss symmetries intermediate between global and local and formalize the notion of dimensional reduction adduced from such symmetries. We apply this generalization to several systems including liquid crystalline phases of Quantum Hall systems, transition metal orbital systems, frustrated spin systems, ( p + ip ) superconducting arrays, and sliding Luttinger liquids. By considering space-time reflection symmetries, we illustrate that several of these systems are dual to each other. In some systems exhibiting these symmetries, low temperature local orders emerge by an "order out of disorder" effect while in other systems, the dimensional reduction precludes standard orders yet allows for multiparticle orders (including those of a topological nature).

Styles APA, Harvard, Vancouver, ISO, etc.

33

GETHING, J. D., A. J. MATTHEWS, A. USHER, M. E. PORTNOI, K. V. KAVOKIN et M. HENINI. « BREAKDOWN OF THE QUANTUM HALL EFFECTS IN HOLE SYSTEMS AT HIGH INDUCED CURRENTS ». International Journal of Modern Physics B 18, n^o 27n29 (30 novembre 2004) : 3537–40. http://dx.doi.org/10.1142/s0217979204026962.

Texte intégral

Résumé :

The magnetisation of two dimensional hole systems in the quantum Hall regime has been studied using a highly-sensitive torsion balance magnetometer. In a time varying magnetic field eddy currents are induced which become large around integer and fractional filling factors where ρxx takes a very low value. The sweep rate and temperature dependence of these induced currents are in good agreement with the model of quantum Hall effect breakdown proposed recently by Matthews et al. This model also allows comparison between the energy gap at different filling factors and so provides a measurement of the fractional quantum Hall effect energy gap, Δ1/3, and the spin split energy gap, g*μ B B.

Styles APA, Harvard, Vancouver, ISO, etc.

34

Nys, Jannes, et Giuseppe Carleo. « Variational solutions to fermion-to-qubit mappings in two spatial dimensions ». Quantum 6 (13 octobre 2022) : 833. http://dx.doi.org/10.22331/q-2022-10-13-833.

Texte intégral

Résumé :

Through the introduction of auxiliary fermions, or an enlarged spin space, one can map local fermion Hamiltonians onto local spin Hamiltonians, at the expense of introducing a set of additional constraints. We present a variational Monte-Carlo framework to study fermionic systems through higher-dimensional (>1D) Jordan-Wigner transformations. We provide exact solutions to the parity and Gauss-law constraints that are encountered in bosonization procedures. We study the t-V model in 2D and demonstrate how both the ground state and the low-energy excitation spectra can be retrieved in combination with neural network quantum state ansatze.

Styles APA, Harvard, Vancouver, ISO, etc.

35

Moutanabbir, Oussama, Patrick Del Vecchio, Anis Attiaoui, Gabriel Fettu, Nicolas Rotaru et Simone Assali. « (Invited) Optoelectronic Quantum Information Processing : An All-Group IV Integrated Platform ». ECS Meeting Abstracts MA2022-02, n^o 32 (9 octobre 2022) : 1207. http://dx.doi.org/10.1149/ma2022-02321207mtgabs.

Texte intégral

Résumé :

Achieving coherent optical photon-to-spin conversion is a long-sought-after strategy for surmounting current fundamental limits in optical schemes that hinder the long-distance distribution of entanglement. Moreover, photon-to-spin interfaces are also essential for a direct mapping of the quantum information encoded in photon flying qubits to stationary spin processors. However, the lack of scalable materials offering an efficient interaction with optical photons along with optimal spin properties remains a formidable obstacle hindering the development of these quantum technological components. With this perspective, this presentation will discuss strategies to address these challenges by leveraging the degrees of freedom offered by group IV (Si)GeSn semiconductors, namely strain and composition, to tailor the electronic structure and eventually fulfill these prerequisites. These innovative systems do not only have the potential to enable coherent photon-to-spin interfaces, but because of their compatibility with the semiconductor industry they will also offer scalability, manufacturability, and cost-effectiveness. We will show that this family of semiconductors provide an additional flexibility to control the charge carrier states and achieve a selective confinement of holes. The latter benefit from a quiet quantum environment that has been at the core of increasingly reliable quantum processors and memories. However, most if not all available experimental studies of two-dimensional gas systems have been thus far focused on heavy-hole (HH) states. This is attributed to the nature of the heterostructures currently available (e.g, Ge/SiGe, InGaAs/GaAs), where compressive strain lifts the valence band degeneracy and leaves HH states energetically well above the light-hole (LH) states. We will demonstrate that tensile strained Ge/GeSn quantum wells alleviate these limitations and allow to selectively confine LH provided the strain is higher than 1%. This requires strain relaxed, high Sn content GeSn buffer layers to be used to grow Ge quantum wells with LH ground state, high g-factor anisotropy, and a tunable splitting of the hole subbands. The optical and electronic properties of these low-dimensional systems will be described and discussed. Spin injection and coherent control will also be addressed. Additionally, qubit designs exploiting the ability to engineer LH states and the Ge large spin-orbit coupling allowing fast all-electrical spin-manipulation schemes will also be presented and discussed.

Styles APA, Harvard, Vancouver, ISO, etc.

36

Senaratne, Ruwan, Danyel Cavazos-Cavazos, Sheng Wang, Feng He, Ya-Ting Chang, Aashish Kafle, Han Pu, Xi-Wen Guan et Randall G. Hulet. « Spin-charge separation in a one-dimensional Fermi gas with tunable interactions ». Science 376, n^o 6599 (17 juin 2022) : 1305–8. http://dx.doi.org/10.1126/science.abn1719.

Texte intégral

Résumé :

Ultracold atoms confined to periodic potentials have proven to be a powerful tool for quantum simulation of complex many-body systems. We confine fermions to one dimension to realize the Tomonaga-Luttinger liquid model, which describes the highly collective nature of their low-energy excitations. We use Bragg spectroscopy to directly excite either the spin or charge waves for various strengths of repulsive interaction. We observe that the velocity of the spin and charge excitations shift in opposite directions with increasing interaction, a hallmark of spin-charge separation. The excitation spectra are in quantitative agreement with the exact solution of the Yang-Gaudin model and the Tomonaga-Luttinger liquid theory. Furthermore, we identify effects of nonlinear corrections to this theory that arise from band curvature and back-scattering.

Styles APA, Harvard, Vancouver, ISO, etc.

37

Hosokoshi, Yuko, Yasuhiro Nakazawa, Katsuya Inoue, Kohichi Takizawa, Hiroki Nakano, Minoru Takahashi et Tsuneaki Goto. « Magnetic properties of low-dimensional quantum spin systems made of stable organic biradicals PNNNO,F2PNNNO,and PIMNO ». Physical Review B 60, n^o 18 (1 novembre 1999) : 12924–32. http://dx.doi.org/10.1103/physrevb.60.12924.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

38

Wolf, B., A. Brühl, J. Magerkurth, S. Zherlitsyn, V. Pashchenko, B. Brendel, G. Margraf et al. « Magnetoelastic and magnetothermal properties of low-dimensional quantum spin systems in high magnetic fields—a case study ». Journal of Magnetism and Magnetic Materials 290-291 (avril 2005) : 411–15. http://dx.doi.org/10.1016/j.jmmm.2004.11.495.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

39

Yamamoto, Shoji. « An Efficient Monte Carlo Approach to Low-Lying Excitations of Quantum Spin Chains ». International Journal of Modern Physics C 08, n^o 03 (juin 1997) : 609–34. http://dx.doi.org/10.1142/s0129183197000527.

Texte intégral

Résumé :

We give a full description of a recently developed efficient Monte Carlo Approach to low-lying excitations of one-dimensional quantum spin systems. The idea is in a word expressed as extracting the lower edge of the excitation spectrum from imaginary-time quantum Monte Carlo data at a sufficiently low temperature. First, the method is applied to the antiferromagnetic Heisenberg chains of S=1/2, 1, 3/2, and 2. In the cases of S=1/2 and S=1, comparing the present results with the previous findings, we discuss the reliability of the method. The spectra for S=3/2 and S=2 turn out to be massless and massive, respectively. In order to demonstrate that our method is very good at treating long chains, we calculate the S=2 chain with length up to 512 spins and give a precise estimate of the Haldane gap. Second, we show its fruitful use in studying quantum critical phenomena of bond-alternating spin chains. Using the conformal invariance of the system as well, we calculate the central charge of the critical S=1 chain, which results in the Gaussian universality class. Third, we study an alternating-spin system composed of two kinds of spins S=1 and 1/2, which shows the ferrimagnetic behavior. We find a quadratic dispersion relation in the small-momentum region. The numerical findings are qualitatively explained well in terms of the spin-wave theory. Finally, we argue a possibility of applying the method to the higher excitations, where we again deal with the S=1 Heisenberg antiferromagnet and inquire further into its unique low-energy structure. All the applications demonstrate the wide applicability of the method and its own advantages.

Styles APA, Harvard, Vancouver, ISO, etc.

40

Fazzini, Serena, et Arianna Montorsi. « Hidden Charge Orders in Low-Dimensional Mott Insulators ». Applied Sciences 9, n^o 4 (22 février 2019) : 784. http://dx.doi.org/10.3390/app9040784.

Texte intégral

Résumé :

The opening of a charge gap driven by interaction is a fingerprint of the transition to a Mott insulating phase. In strongly correlated low-dimensional quantum systems, it can be associated to the ordering of hidden non-local operators. For Fermionic 1D models, in the presence of spin–charge separation and short-ranged interaction, a bosonization analysis proves that such operators are the parity and/or string charge operators. In fact, a finite fractional non-local parity charge order is also capable of characterizing some two-dimensional Mott insulators, in both the Fermionic and the bosonic cases. When string charge order takes place in 1D, degenerate edge modes with fractional charge appear, peculiar of a topological insulator. In this article, we review the above framework, and we test it to investigate through density-matrix-renormalization-group (DMRG) numerical analysis the robustness of both hidden orders at half-filling in the 1D Fermionic Hubbard model extended with long range density-density interaction. The preliminary results obtained at finite size including several neighbors in the case of dipolar, screened and unscreened repulsive Coulomb interactions, confirm the phase diagram of the standard extended Hubbard model. Besides the trivial Mott phase, the bond ordered and charge density wave insulating phases are also not destroyed by longer ranged interaction, and still manifest hidden non-local orders.

Styles APA, Harvard, Vancouver, ISO, etc.

41

Azzouz, Mohamed. « Topological Monopoles in Quantum Antiferromagnets ». Symmetry 11, n^o 3 (5 mars 2019) : 323. http://dx.doi.org/10.3390/sym11030323.

Texte intégral

Résumé :

While the observation of magnetic monopoles has defied all experimental attempts in high-energy physics and astrophysics, sound theoretical approaches predict that they should exist, and they have indeed been observed as quasiparticle excitations in certain condensed-matter systems. This indicates that, even though they are not ubiquitous contrary to electrons, it is possible to get them as excitations above a background. In this report, we show that phonons or lattice shear strain generate topological monopoles in some low-dimensional quantum antiferromagnets. For the Heisenberg ladder, phonons are found to generate topological monopoles with nonzero density due to quantum spin fluctuations. For the four-leg Heisenberg tube, longitudinal shear stress generates topological monopoles with density proportional to the strain deformation. The present theory is based on mapping the spin degrees of freedom onto spinless fermions using the generalized Jordan–Wigner transformation in dimensions higher than one. The effective magnetic field generated by the motion of the spinless fermions has nonzero divergence when phonons or shear stress are present. A possible material where the present kind of monopoles could be observed is BiCu 2 PO 6 .

Styles APA, Harvard, Vancouver, ISO, etc.

42

Brown, Peter T., Debayan Mitra, Elmer Guardado-Sanchez, Peter Schauß, Stanimir S. Kondov, Ehsan Khatami, Thereza Paiva, Nandini Trivedi, David A. Huse et Waseem S. Bakr. « Spin-imbalance in a 2D Fermi-Hubbard system ». Science 357, n^o 6358 (28 septembre 2017) : 1385–88. http://dx.doi.org/10.1126/science.aam7838.

Texte intégral

Résumé :

The interplay of strong interactions and magnetic fields gives rise to unusual forms of superconductivity and magnetism in quantum many-body systems. Here, we present an experimental study of the two-dimensional Fermi-Hubbard model—a paradigm for strongly correlated fermions on a lattice—in the presence of a Zeeman field and varying doping. Using site-resolved measurements, we revealed anisotropic antiferromagnetic correlations, a precursor to long-range canted order. We observed nonmonotonic behavior of the local polarization with doping for strong interactions, which we attribute to the evolution from an antiferromagnetic insulator to a metallic phase. Our results pave the way to experimentally mapping the low-temperature phase diagram of the Fermi-Hubbard model as a function of both doping and spin polarization, for which many open questions remain.

Styles APA, Harvard, Vancouver, ISO, etc.

43

Masuda, Hidetoshi, Hideaki Sakai, Masashi Tokunaga, Yuichi Yamasaki, Atsushi Miyake, Junichi Shiogai, Shintaro Nakamura et al. « Quantum Hall effect in a bulk antiferromagnet EuMnBi2 with magnetically confined two-dimensional Dirac fermions ». Science Advances 2, n^o 1 (janvier 2016) : e1501117. http://dx.doi.org/10.1126/sciadv.1501117.

Texte intégral

Résumé :

For the innovation of spintronic technologies, Dirac materials, in which low-energy excitation is described as relativistic Dirac fermions, are one of the most promising systems because of the fascinating magnetotransport associated with extremely high mobility. To incorporate Dirac fermions into spintronic applications, their quantum transport phenomena are desired to be manipulated to a large extent by magnetic order in a solid. We report a bulk half-integer quantum Hall effect in a layered antiferromagnet EuMnBi2, in which field-controllable Eu magnetic order significantly suppresses the interlayer coupling between the Bi layers with Dirac fermions. In addition to the high mobility of more than 10,000 cm2/V s, Landau level splittings presumably due to the lifting of spin and valley degeneracy are noticeable even in a bulk magnet. These results will pave a route to the engineering of magnetically functionalized Dirac materials.

Styles APA, Harvard, Vancouver, ISO, etc.

44

Chen Xiao-Bin et Duan Wen-Hui. « Quantum thermal transport and spin thermoelectrics in low-dimensional nano systems : application of nonequilibrium Green's function method ». Acta Physica Sinica 64, n^o 18 (2015) : 186302. http://dx.doi.org/10.7498/aps.64.186302.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

45

LEE, C. W. H., et S. G. RAJEEV. « A REVIEW OF SYMMETRY ALGEBRAS OF QUANTUM MATRIX MODELS IN THE LARGE N LIMIT ». International Journal of Modern Physics A 14, n^o 28 (10 novembre 1999) : 4395–455. http://dx.doi.org/10.1142/s0217751x99002074.

Texte intégral

Résumé :

This is a review article in which we will introduce, in a unifying fashion and with more intermediate steps in some difficult calculations, two infinite-dimensional Lie algebras of quantum matrix models, one for the open string sector and the other for the closed string sector. Physical observables of quantum matrix models in the large N limit can be expressed as elements of these Lie algebras. We will see that both algebras arise as quotient algebras of a larger Lie algebra. We will also discuss some properties of these Lie algebras not published elsewhere yet, and briefly review their relationship with well-known algebras like the Cuntz algebra, the Witt algebra and the Virasoro algebra. We will also review how the Yang–Mills theory, various low energy effective models of string theory, quantum gravity, string-bit models, and the quantum spin chain models can be formulated as quantum matrix models. Studying these algebras thus help us understand the common symmetry of these physical systems.

Styles APA, Harvard, Vancouver, ISO, etc.

46

Bykov, Maxim, Elena Bykova, Leonid Dubrovinsky, Michael Hanfland, Hanns-Peter Liermann, Reinhard Kremer et Sander van Smaalen. « Pressure-induced normal-incommensurate-commensurate phase transitions in TiPO4 ». Acta Crystallographica Section A Foundations and Advances 70, a1 (5 août 2014) : C263. http://dx.doi.org/10.1107/s2053273314097368.

Texte intégral

Résumé :

The complex interplay between spin, charge, orbital, and lattice degrees of freedom has made low-dimensional quantum spin magnets with strong antiferromagnetic (AF) spin-exchange coupling prime candidates for studying unusual magnetic phenomena. A progressive spin-lattice dimerization in one-dimensional AF Heisenberg chains, which occurs below a critical temperature and induces a singlet ground state with a magnetic gap, is commonly referred to as spin-Peierls (SP) transition. Recently, the compounds TiOX (X = Cl, Br) and TiPO4have been intensively investigated due to their unconventional behavior [1,2]. Unlike standard SP systems, TiOX and TiPO4undergo a sequence of normal-incommensurate-commensurate phase transitions on cooling at remarkably high transition temperatures. The transition temperatures are related to the direct exchange interactions between Ti ions, which increases strongly with decreasing the distance between the Ti ions, and therefore is very sensitive to the applied hydrostatic pressure. We have performed pressure-dependent single-crystal X-ray diffraction of TiPO4using synchrotron radiation. TiPO4undergoes a pressure-induced pahse transiton towards an incommensurate phase already below 10 GPa. This transformation is followed by the lock-in phase transition to the dimerized SP phase. Both structures are analogous to those at low temperatures, but reveal significantly larger modulation amplitudes. In this contribution we will present the detailed discussion of the high-pressure structures of TiPO4and their behavior on compression. Furthermore, similarities and differences of high-pressure phase diagrams of TiOCl and TiPO4and discrepancies between predicted and observed structures will be considered.

Styles APA, Harvard, Vancouver, ISO, etc.

47

Hsu, Chen-Hsuan, Peter Stano, Jelena Klinovaja et Daniel Loss. « Helical liquids in semiconductors ». Semiconductor Science and Technology 36, n^o 12 (28 octobre 2021) : 123003. http://dx.doi.org/10.1088/1361-6641/ac2c27.

Texte intégral

Résumé :

Abstract One-dimensional helical liquids can appear at boundaries of certain condensed matter systems. Two prime examples are the edge of a quantum spin Hall insulator and the hinge of a three-dimensional second-order topological insulator. For these materials, the presence of a helical state at the boundary serves as a signature of their nontrivial electronic bulk topology. Additionally, these boundary states are of interest themselves, as a novel class of strongly correlated low-dimensional systems with interesting potential applications. Here, we review existing results on such helical liquids in semiconductors. Our focus is on the theory, though we confront it with existing experiments. We discuss various aspects of the helical liquids, such as their realization, topological protection and stability, or possible experimental characterization. We lay emphasis on the hallmark of these states, being the prediction of a quantized electrical conductance. Since so far reaching a well-quantized conductance has remained challenging experimentally, a large part of the review is a discussion of various backscattering mechanisms which have been invoked to explain this discrepancy. Finally, we include topics related to proximity-induced topological superconductivity in helical states, as an exciting application toward topological quantum computation with the resulting Majorana bound states.

Styles APA, Harvard, Vancouver, ISO, etc.

48

Villarreal, Renan. « (Invited, Digital Presentation) Single-Atom Quantum Magnetism in 2D Materials ». ECS Meeting Abstracts MA2022-01, n^o 12 (7 juillet 2022) : 874. http://dx.doi.org/10.1149/ma2022-0112874mtgabs.

Texte intégral

Résumé :

With the advent of 2D materials, the playground to study spins in dilute and non-dilute phases has expanded. This is appealing for utilizing the additional degrees of freedom of electron systems such as spin and valley and, from the fundamental point of view, to better understand atomic scale magnetic phenomena in low dimensional materials. Dilute magnetism in 2D materials can lead to complex magnetic phenomena (e.g., Kondo effect, RKKY-interactions, quantum relaxation and coherence), with potential for applications in spintronics (e.g., spin FETs) and quantum technologies (e.g., single-atom quantum memories). We are investigating how to selectively incorporate substitutional magnetic atoms (3d transition metals and 4f rare earths) in 2D materials, using ultra low energy ion implantation, and we characterize their structural, electronic, and magnetic properties [1]. Ultra-low energy (ULE) ion implantation allows us to precisely tune the kinetic energy of the ions, providing control over the form of incorporation and concentration while preserving the structural and electronic properties of graphene. Our approach is based on a wide range of characterization techniques (structural and electronic), including scanning tunneling microscopy and spectroscopy (STM/STS), Raman spectroscopy, synchrotron-based X-ray photoelectron spectroscopy (XPS), angle-resolved photoemission spectroscopy (ARPES), X-ray magnetic circular dichroism (XMCD), among others. These experimental studies are complemented by density functional theory (DFT) and molecular dynamics (MD) simulations. The new insights provided by our work establish a framework for the controlled incorporation of magnetic dopants in 2D materials, using ULE ion implantation. [1] P. C. Lin et al., ACS Nano 15(3), 5449-5458 (2021).

Styles APA, Harvard, Vancouver, ISO, etc.

49

Mukhin, S. I., et S. I. Matveenko. « Stripe Phase : Analytical Results for Weakly Coupled Repulsive Hubbard Model ». International Journal of Modern Physics B 17, n^o 21 (20 août 2003) : 3749–83. http://dx.doi.org/10.1142/s0217979203022726.

Texte intégral

Résumé :

Motivated by the stripe developments in cuprates, we review analytical results for the spin-charge solitonic superstructures derived in the framework of the Hubbard model in our studies of weakly coupled (quasi) one-dimensional repulsive electron systems on a lattice. These results demonstrate that close to half filling, in the high temperature regime above the mean field transition temperature, short range repulsions favor charge density fluctuations with wavevectors bearing special relations with those of the spin density fluctuations. In the low temperature regime, besides the wavevectors, mutual phases of the charge and spin densities also become coupled due to a quantum interference phenomenon, leading to the stripe phase instability. It is shown that away from half filling, periodic lattice potential causes cooperative condensation of the spin and charge superlattices. "Switching off" this potential leads to the vanishing of the stripe order. The leading spin-charge coupling term in the effective Landau functional is derived microscopically. Results of the 1D renormalization group ("parquet") analysis away from half filling are also presented. They reveal transient-scale correlations resembling the mean-field pattern. Possible correspondence of our theory with the experimental data on stripe phase in high Tc cuprates is discussed.

Styles APA, Harvard, Vancouver, ISO, etc.

50

WEN, X. G. « TOPOLOGICAL ORDERS IN RIGID STATES ». International Journal of Modern Physics B 04, n^o 02 (février 1990) : 239–71. http://dx.doi.org/10.1142/s0217979290000139.

Texte intégral

Résumé :

We study a new kind of ordering — topological order — in rigid states (the states with no local gapless excitations). We concentrate on characterization of the different topological orders. As an example we discuss in detail chiral spin states of 2 + 1 dimensional spin systems. Chiral spin states are described by the topological Chern-Simons theories in the continuum limit. We show that the topological orders can be characterized by a non-Abelian gauge structure over the moduli space which parametrizes a family of the model Hamiltonians supporting topologically ordered ground states. In 2 + 1 dimensions, the non-Abelian gauge structure determines possible fractional statistics of the quasi-particle excitations over the topologically ordered ground states. The dynamics of the low lying global excitations is shown to be independent of random spatial dependent perturbations. The ground state degeneracy and the non-Abelian gauge structures discussed in this paper are very robust, even against those perturbations that break translation symmetry. We also discuss the symmetry properties of the degenerate ground states of chiral spin states. We find that some degenerate ground states of chiral spin states on torus carry non-trivial quantum numbers of the 90° rotation.

Styles APA, Harvard, Vancouver, ISO, etc.

Articles de revues sur le sujet « Low Dimensional Quantum Spin Systems »

Créez une référence correcte selon les styles APA, MLA, Chicago, Harvard et plusieurs autres