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Автор: Grafiati

Опубліковано: 6 вересня 2023

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1

Zvyagin, A. A. "Ground state of the biaxial spin-1/2 open chain." Low Temperature Physics 48, no. 5 (May 2022): 383–88. http://dx.doi.org/10.1063/10.0010202.

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The ground state behavior of the biaxial spin-1/2 chain with free open edges is studied. Using the exact Bethe ansatz solution we show that there can exist boundary bound states for many finite values of the exchange coupling constants. The non-trivial interaction between spins produces charging of the vacua of the model and boundary bound states. Our theory also describes the behavior of the spinless fermion chain with pairing (the Kitaev chain) and an interaction between fermions at neighboring sites for free open boundaries. Therefore, the simple case of noninteracting fermions simplest boundary states are Majorana edge modes.

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2

Jaworowski, Błażej, and Paweł Hawrylak. "Quantum Bits with Macroscopic Topologically Protected States in Semiconductor Devices." Applied Sciences 9, no. 3 (January 30, 2019): 474. http://dx.doi.org/10.3390/app9030474.

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Current computers are made of semiconductors. Semiconductor technology enables realization of microscopic quantum bits based on electron spins of individual electrons localized by gates in field effect transistors. This results in very fragile quantum processors prone to decoherence. Here, we discuss an alternative approach to constructing qubits using macroscopic and topologically protected states realized in semiconductor devices. First, we discuss a synthetic spin-1 chain realized in an array of quantum dots in a semiconductor nanowire or in a field effect transitor. A synthetic spin-1 chain is characterized by two effective edge quasiparticles with spin 1 / 2 protected from decoherence by topology and Haldane gap. The spin-1 / 2 quasiparticles of Haldane phase form the basis of a macroscopic singlet-triplet qubit. We compare the spin one chain with a Kitaev chain. Its edge states are Majorana zero modes, possessing non-Abelian fractional statistics. They can be used to encode the quantum information using the braiding processes, i.e., encircling one particle by another, which do not depend on the details of the particle trajectory and thus are protected from decoherence.

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3

Vlasov, Alexander Yurievich. "Clifford Algebras, Spin Groups and Qubit Trees." Quanta 11, no. 1 (December 1, 2022): 97–114. http://dx.doi.org/10.12743/quanta.v11i1.199.

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Representations of Spin groups and Clifford algebras derived from the structure of qubit trees are introduced in this work. For ternary trees the construction is more general and reduction to binary trees is formally defined by deletion of superfluous branches. The usual Jordan–Wigner construction also may be formally obtained in this approach by bringing the process up to trivial qubit chain (trunk). The methods can also be used for effective simulation of some quantum circuits corresponding to the binary tree structure. The modeling of more general qubit trees, as well as the relationship with the mapping used in the Bravyi–Kitaev transformation, are also briefly discussed.Quanta 2022; 11: 97–114.

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4

Güngördü, Utkan, and Alexey A. Kovalev. "Majorana bound states with chiral magnetic textures." Journal of Applied Physics 132, no. 4 (July 28, 2022): 041101. http://dx.doi.org/10.1063/5.0097008.

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The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana fermions, usually termed as Majorana bound states (MBSs), in condensed matter systems with magnetic textures. We begin by considering the Kitaev chain model of “spinless” fermions and show how two “half” fermions can appear at chain ends due to interactions. By considering this model and its two-dimensional generalization, we emphasize intricate relation between topological superconductivity and possible realizations of MBS. We further discuss how “spinless” fermions can be realized in more physical systems, e.g., by employing the spin-momentum locking. Next, we demonstrate how magnetic textures can be used to induce synthetic or fictitious spin–orbit interactions, and, thus, stabilize MBS. We describe a general approach that works for arbitrary textures and apply it to skyrmions. We show how MBS can be stabilized by elongated skyrmions, certain higher order skyrmions, and chains of skyrmions. We also discuss how braiding operations can be performed with MBS stabilized on magnetic skyrmions. This Tutorial is aimed at students at the graduate level.

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5

Peotta, Sebastiano, Leonardo Mazza, Ettore Vicari, Marco Polini, Rosario Fazio, and Davide Rossini. "The XYZ chain with Dzyaloshinsky–Moriya interactions: from spin–orbit-coupled lattice bosons to interacting Kitaev chains." Journal of Statistical Mechanics: Theory and Experiment 2014, no. 9 (September 8, 2014): P09005. http://dx.doi.org/10.1088/1742-5468/2014/09/p09005.

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6

Agrapidis, Cliò Efthimia, Jeroen van den Brink, and Satoshi Nishimoto. "Numerical Study of the Kitaev-Heisenberg chain as a spin model of the K-intercalated RuCl3." Journal of Physics: Conference Series 969 (March 2018): 012112. http://dx.doi.org/10.1088/1742-6596/969/1/012112.

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7

Mazziotti, Maria, Niccolò Scopigno, Marco Grilli, and Sergio Caprara. "Majorana Fermions in One-Dimensional Structures at LaAlO3/SrTiO3 Oxide Interfaces." Condensed Matter 3, no. 4 (October 29, 2018): 37. http://dx.doi.org/10.3390/condmat3040037.

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We study one-dimensional structures that may be formed at the LaAlO 3 /SrTiO 3 oxide interface by suitable top gating. These structures are modeled via a single-band model with Rashba spin-orbit coupling, superconductivity and a magnetic field along the one-dimensional chain. We first discuss the conditions for the occurrence of a topological superconducting phase and the related formation of Majorana fermions at the chain endpoints, highlighting a close similarity between this model and the Kitaev model, which also reflects in a similar condition the formation of a topological phase. Solving the model in real space, we also study the spatial extension of the wave function of the Majorana fermions and how this increases with approaching the limit condition for the topological state. Using a scattering matrix formalism, we investigate the stability of the Majorana fermions in the presence of disorder and discuss the evolution of the topological phase with increasing disorder.

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8

Kotetes, Panagiotis. "Diagnosing topological phase transitions in 1D superconductors using Berry singularity markers." Journal of Physics: Condensed Matter 34, no. 17 (February 25, 2022): 174003. http://dx.doi.org/10.1088/1361-648x/ac4f1e.

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Abstract In this work I demonstrate how to characterize topological phase transitions in BDI symmetry class superconductors (SCs) in 1D, using the recently introduced approach of Berry singularity markers (BSMs). In particular, I apply the BSM method to the celebrated Kitaev chain model, as well as to a variant of it, which contains both nearest and next nearest neighbor equal spin pairings. Depending on the situation, I identify pairs of external fields which can detect the topological charges of the Berry singularities which are responsible for the various topological phase transitions. These pairs of fields consist of either a flux knob which controls the supercurrent flow through the SC, or, strain, combined with a field which can tune the chemical potential of the system. Employing the present BSM approach appears to be within experimental reach for topological nanowire hybrids.

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9

Zazunov, Alex, Albert Iks, Miguel Alvarado, Alfredo Levy Yeyati, and Reinhold Egger. "Josephson effect in junctions of conventional and topological superconductors." Beilstein Journal of Nanotechnology 9 (June 6, 2018): 1659–76. http://dx.doi.org/10.3762/bjnano.9.158.

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We present a theoretical analysis of the equilibrium Josephson current-phase relation in hybrid devices made of conventional s-wave spin-singlet superconductors (S) and topological superconductor (TS) wires featuring Majorana end states. Using Green’s function techniques, the topological superconductor is alternatively described by the low-energy continuum limit of a Kitaev chain or by a more microscopic spinful nanowire model. We show that for the simplest S–TS tunnel junction, only the s-wave pairing correlations in a spinful TS nanowire model can generate a Josephson effect. The critical current is much smaller in the topological regime and exhibits a kink-like dependence on the Zeeman field along the wire. When a correlated quantum dot (QD) in the magnetic regime is present in the junction region, however, the Josephson current becomes finite also in the deep topological phase as shown for the cotunneling regime and by a mean-field analysis. Remarkably, we find that the S–QD–TS setup can support φ0-junction behavior, where a finite supercurrent flows at vanishing phase difference. Finally, we also address a multi-terminal S–TS–S geometry, where the TS wire acts as tunable parity switch on the Andreev bound states in a superconducting atomic contact.

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10

Yang, Wang, Alberto Nocera, Erik S. Sørensen, Hae-Young Kee, and Ian Affleck. "Classical spin order near the antiferromagnetic Kitaev point in the spin- 12 Kitaev-Gamma chain." Physical Review B 103, no. 5 (February 24, 2021). http://dx.doi.org/10.1103/physrevb.103.054437.

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11

Gordon, Jacob S., and Hae-Young Kee. "Insights into the anisotropic spin- S Kitaev chain." Physical Review Research 4, no. 1 (March 16, 2022). http://dx.doi.org/10.1103/physrevresearch.4.013205.

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12

Steinigeweg, Robin, and Wolfram Brenig. "Energy dynamics in the Heisenberg-Kitaev spin chain." Physical Review B 93, no. 21 (June 20, 2016). http://dx.doi.org/10.1103/physrevb.93.214425.

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13

Shibata, Naoyuki, and Hosho Katsura. "Dissipative spin chain as a non-Hermitian Kitaev ladder." Physical Review B 99, no. 17 (May 10, 2019). http://dx.doi.org/10.1103/physrevb.99.174303.

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14

Vimal, Vimalesh Kumar, H. Wanare, and V. Subrahmanyam. "Loschmidt echo and momentum distribution in a Kitaev spin chain." Physical Review A 106, no. 3 (September 28, 2022). http://dx.doi.org/10.1103/physreva.106.032221.

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15

You, Wen-Long, Gaoyong Sun, Jie Ren, Wing Chi Yu, and Andrzej M. Oleś. "Quantum phase transitions in the spin-1 Kitaev-Heisenberg chain." Physical Review B 102, no. 14 (October 23, 2020). http://dx.doi.org/10.1103/physrevb.102.144437.

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16

Vimal, Vimalesh Kumar, and V. Subrahmanyam. "Quantum correlations and entanglement in a Kitaev-type spin chain." Physical Review A 98, no. 5 (November 5, 2018). http://dx.doi.org/10.1103/physreva.98.052303.

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17

Sørensen, Erik S., Jacob Gordon, Jonathon Riddell, Tianyi Wang, and Hae-Young Kee. "Field-induced chiral soliton phase in the Kitaev spin chain." Physical Review Research 5, no. 1 (February 27, 2023). http://dx.doi.org/10.1103/physrevresearch.5.l012027.

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18

Vargas-Calderón, Vladimir, Herbert Vinck-Posada, and Fabio A. González. "An empirical study of quantum dynamics as a ground state problem with neural quantum states." Quantum Information Processing 22, no. 4 (April 7, 2023). http://dx.doi.org/10.1007/s11128-023-03902-9.

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AbstractWe consider the Feynman–Kitaev formalism applied to a spin chain described by the transverse-field Ising model. This formalism consists of building a Hamiltonian whose ground state encodes the time evolution of the spin chain at discrete time steps. To find this ground state, variational wave functions parameterised by artificial neural networks—also known as neural quantum states (NQSs)—are used. Our work focuses on assessing, in the context of the Feynman–Kitaev formalism, two properties of NQSs: expressivity (the possibility that variational parameters can be set to values such that the NQS is faithful to the true ground state of the system) and trainability (the process of reaching said values). We find that the considered NQSs are capable of accurately approximating the true ground state of the system, i.e. they are expressive enough ansätze. However, extensive hyperparameter tuning experiments show that, empirically, reaching the set of values for the variational parameters that correctly describe the ground state becomes ever more difficult as the number of time steps increase because the true ground state becomes more entangled, and the probability distribution starts to spread across the Hilbert space canonical basis.

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19

Kumar Vimal, Vimalesh, and V. Subrahmanyam. "Magnetization revivals and dynamics of quantum correlations in a Kitaev spin chain." Physical Review A 102, no. 1 (July 7, 2020). http://dx.doi.org/10.1103/physreva.102.012406.

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20

Wouters, Jurriaan, Hosho Katsura, and Dirk Schuricht. "Interrelations among frustration-free models via Witten's conjugation." SciPost Physics Core 4, no. 4 (October 14, 2021). http://dx.doi.org/10.21468/scipostphyscore.4.4.027.

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We apply Witten’s conjugation argument [Nucl. Phys. B 202, 253 (1982)] to spin chains, where it allows us to derive frustration-free systems and their exact ground states from known results. We particularly focus on \mathbb{Z}_pℤp-symmetric models, with the Kitaev and Peschel–Emery line of the axial next-nearest neighbour Ising (ANNNI) chain being the simplest examples. The approach allows us to treat two \mathbb{Z}_3ℤ3-invariant frustration-free parafermion chains, recently derived by Iemini et al. [Phys. Rev. Lett. 118, 170402 (2017)] and Mahyaeh and Ardonne [Phys. Rev. B 98, 245104 (2018)], respectively, in a unified framework. We derive several other frustration-free models and their exact ground states, including \mathbb{Z}_4ℤ4- and \mathbb{Z}_6ℤ6-symmetric generalisations of the frustration-free ANNNI chain.

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21

Yang, Wang, Alberto Nocera, and Ian Affleck. "Comprehensive study of the phase diagram of the spin- 12 Kitaev-Heisenberg-Gamma chain." Physical Review Research 2, no. 3 (August 19, 2020). http://dx.doi.org/10.1103/physrevresearch.2.033268.

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22

Yang, Wang, Alberto Nocera, Tarun Tummuru, Hae-Young Kee, and Ian Affleck. "Phase Diagram of the Spin- 1/2 Kitaev-Gamma Chain and Emergent SU(2) Symmetry." Physical Review Letters 124, no. 14 (April 10, 2020). http://dx.doi.org/10.1103/physrevlett.124.147205.

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23

Luo, Qiang, Shijie Hu, Jinbin Li, Jize Zhao, Hae-Young Kee, and Xiaoqun Wang. "Spontaneous dimerization, spin-nematic order, and deconfined quantum critical point in a spin-1 Kitaev chain with tunable single-ion anisotropy." Physical Review B 107, no. 24 (June 22, 2023). http://dx.doi.org/10.1103/physrevb.107.245131.

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24

Mishra, Sparsh, Shun Tamura, Akito Kobayashi, and Yukio Tanaka. "Impact of impurity scattering on odd-frequency spin-triplet pairing near the edge of the Kitaev chain." Physical Review B 103, no. 2 (January 5, 2021). http://dx.doi.org/10.1103/physrevb.103.024501.

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25

Macêdo, Rafael A., Flávia B. Ramos, and Rodrigo G. Pereira. "Continuous phase transition from a chiral spin state to collinear magnetic order in a zigzag chain with Kitaev interactions." Physical Review B 105, no. 20 (May 31, 2022). http://dx.doi.org/10.1103/physrevb.105.205144.

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26

Pan, Haining, and Sankar Das Sarma. "Majorana nanowires, Kitaev chains, and spin models." Physical Review B 107, no. 3 (January 31, 2023). http://dx.doi.org/10.1103/physrevb.107.035440.

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27

You, Wen-Long, Zhuan Zhao, Jie Ren, Gaoyong Sun, Liangsheng Li, and Andrzej M. Oleś. "Quantum many-body scars in spin-1 Kitaev chains." Physical Review Research 4, no. 1 (February 10, 2022). http://dx.doi.org/10.1103/physrevresearch.4.013103.

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28

Sørensen, Erik S., Jonathon Riddell, and Hae-Young Kee. "Islands of chiral solitons in integer-spin Kitaev chains." Physical Review Research 5, no. 1 (March 28, 2023). http://dx.doi.org/10.1103/physrevresearch.5.013210.

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29

Yang, Wang, Alberto Nocera, Paul Herringer, Robert Raussendorf, and Ian Affleck. "Symmetry analysis of bond-alternating Kitaev spin chains and ladders." Physical Review B 105, no. 9 (March 25, 2022). http://dx.doi.org/10.1103/physrevb.105.094432.

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30

Subrahmanyam, V. "Block entropy for Kitaev-type spin chains in a transverse field." Physical Review A 88, no. 3 (September 16, 2013). http://dx.doi.org/10.1103/physreva.88.032315.

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31

Wang, Qingzhen, Sebastiaan L. D. ten Haaf, Ivan Kulesh, Di Xiao, Candice Thomas, Michael J. Manfra, and Srijit Goswami. "Triplet correlations in Cooper pair splitters realized in a two-dimensional electron gas." Nature Communications 14, no. 1 (August 12, 2023). http://dx.doi.org/10.1038/s41467-023-40551-z.

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AbstractCooper pairs occupy the ground state of superconductors and are typically composed of maximally entangled electrons with opposite spin. In order to study the spin and entanglement properties of these electrons, one must separate them spatially via a process known as Cooper pair splitting (CPS). Here we provide the first demonstration of CPS in a semiconductor two-dimensional electron gas (2DEG). By coupling two quantum dots to a superconductor-semiconductor hybrid region we achieve efficient Cooper pair splitting, and clearly distinguish it from other local and non-local processes. When the spin degeneracy of the dots is lifted, they can be operated as spin-filters to obtain information about the spin of the electrons forming the Cooper pair. Not only do we observe a near perfect splitting of Cooper pairs into opposite-spin electrons (i.e. conventional singlet pairing), but also into equal-spin electrons, thus achieving triplet correlations between the quantum dots. Importantly, the exceptionally large spin-orbit interaction in our 2DEGs results in a strong triplet component, comparable in amplitude to the singlet pairing. The demonstration of CPS in a scalable and flexible platform provides a credible route to study on-chip entanglement and topological superconductivity in the form of artificial Kitaev chains.

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32

Xu, Haoting, and Hae-Young Kee. "Creating long-range entangled Majorana pairs: From spin- 12 twisted Kitaev to generalized XY chains." Physical Review B 107, no. 13 (April 26, 2023). http://dx.doi.org/10.1103/physrevb.107.134435.

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33

Yang, Wang, Chao Xu, Alberto Nocera, and Ian Affleck. "Origin of nonsymmorphic bosonization formulas in generalized antiferromagnetic Kitaev spin- 12 chains from a renormalization-group perspective." Physical Review B 106, no. 6 (August 22, 2022). http://dx.doi.org/10.1103/physrevb.106.064425.

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34

Naaijkens, Pieter, and Yoshiko Ogata. "The Split and Approximate Split Property in 2D Systems: Stability and Absence of Superselection Sectors." Communications in Mathematical Physics, March 28, 2022. http://dx.doi.org/10.1007/s00220-022-04356-3.

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AbstractThe split property of a pure state for a certain cut of a quantum spin system can be understood as the entanglement between the two subsystems being weak. From this point of view, we may say that if it is not possible to transform a state $$\omega $$ ω via sufficiently local automorphisms (in a sense that we will make precise) into a state satisfying the split property, then the state $$\omega $$ ω has a long-range entanglement. It is well known that in 1D, gapped ground states have the split property with respect to cutting the system into left and right half-chains. In 2D, however, the split property fails to hold for interesting models such as Kitaev’s toric code. Here we show that this failure is the reason that anyons can exist in that model. There is a folklore saying that the existence of anyons, like in the toric code model, implies long-range entanglement of the state. In this paper, we prove this folklore in an infinite dimensional setting. More precisely, we show that long-range entanglement, in a way that we will define precisely, is a necessary condition to have non-trivial superselection sectors. Anyons in particular give rise to such non-trivial sectors. States with the split property for cones, on the other hand, do not admit non-trivial sectors. A key technical ingredient of our proof is that under suitable assumptions on locality, the automorphisms generated by local interactions can be “approximately factorized.” That is, they can be written as the tensor product of automorphisms localized in a cone and its complement respectively, followed by an automorphism acting near the “boundary” of $$\Lambda $$ Λ , and conjugation with a unitary. This result may be of independent interest. This technique also allows us to prove that the approximate split property, a weaker version of the split property that is satisfied in e.g. the toric code, is stable under applying such automorphisms.

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