Influence of Topological Phase Transition on Entanglement in the Spin-1 Antiferromagnetic XX Model in Two Dimensions
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Influence of Topological Phase Transition on Entanglement in the Spin‑1 Antiferromagnetic XX Model in Two Dimensions L. S. Lima1 Received: 23 March 2020 / Accepted: 28 July 2020 / Published online: 15 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we study the von Neumann entanglement entropy as a measure of the quantum entanglement in the spin-1 two-dimensional XX model with single-ion anisotropy. We use the bond operator formalism and consider the range of large anisotropy D and in the neighborhood of the critical point Dc . One discusses the influence of the Berezinskii–Kosterlitz–Thouless phase transition (BKT) that occurs at critical anisotropy point Dc , or the transition of the topological order of vortices and disordered phase on quantum entanglement. Keywords Entanglement · BKT transition · XX model
1 Introduction The quantum anisotropic two-dimensional XX model with single-ion anisotropy on square lattice is a very important model in condensed matter physics due to wellknown Berezinskii–Kosterlitz–Thouless transition [1, 2] (BKT transition) that occurs at a critical anisotropy parameter Dc and temperature TBKT . It is well known that a topological order of vortices arises in the system for D < Dc and T ≤ TBKT in the phase diagram (T vs. D) of the model [3–12]. Since two-dimensional XXZ model is a generalization of the XX model, it has been many studied in the literature using both analytical and numerical techniques, in addition to a large experimental effort [3, 5–9, 13–16]. For larger values of single-ion anisotropy D, the system is in the disordered phase [15]. For D ≠ 0 at T = 0 , the phase diagram of this model (T vs. D) has been studied via Schwinger’s boson method at Ref. [4] On the other side, the concept of quantum entanglement belongs to Schrödinger [17, 18] in his reply to famous paper by Einstein et al. [19], where the basic * L. S. Lima [email protected]; [email protected] 1
Department of Physics, Federal Education Center Technological of Minas Gerais, Belo Horizonte, MG 30510‑000, Brazil
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Journal of Low Temperature Physics (2020) 201:515–525
observation made by them was that if the global state of a system is chosen suitably, then it is possible to change and to some extent to choose the state assignment in laboratory A by performing operations in laboratory B. The physicists in laboratory A will be uncertain of this until they are told, but they can check in retrospect that the experiments they performed were consistent with the state assignment from afarment. The opinion considered by Einstein was that on one supposition, we should absolutely to be sure of that the real factual situation of the system S2 is independent of what is done with the system S1 which is spatially separated from the former. Then, we seem us to be forced to the conclusion that quantum mechanics is an incomplete theory in the sense that its initial state assignment does not fully describe the factual situation in labo
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