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Entropy
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Entanglement Entropy and Quantum Phase Transition
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Entanglement Entropy and Quantum Phase Transition

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (15 April 2025) | Viewed by 8277

Special Issue Editors

Prof. Dr. Longwen Zhou

E-Mail Website
Guest Editor
Department of Physics, College of Information Science and Engineering, Ocean University of China, Qingdao 266100, China
Interests: quantum dynamics; Floquet system; non-Hermitian physics; topological phases
Prof. Dr. Dajian Zhang

E-Mail Website
Guest Editor
Department of Physics, Shandong University, Jinan 250100, China
Interests: quantum information

Special Issue Information

Dear Colleagues,

Entanglement represents correlations in composite quantum systems with no classical counterparts. As one of the most fascinating features of quantum physics, the presence of entanglement not only deepens our understanding of microscopic worlds, but also provides us with an indispensable resource for the acceleration of quantum computation and commutation. The 2022 Nobel Prize in Physics, which was awarded for experiments establishing entanglement between photons and disproving Bell inequalities, will further motivate our study of entanglement and its characterizations (e.g., entanglement entropy in quantum information science and quantum matter). A quantum phase transition is driven by quantum fluctuations at zero temperature and induced by changing a system parameter such as magnetic field or pressure. Going through a quantum phase transition, the many-body ground state of a system will experience qualitative changes. Intrinsic quantum aspects of these changes can be revealed by the entanglement and topological structures of the underlying wave-function in the critical regime. For example, the bipartite entanglement entropy could diverge at a critical point, and decays monotonically away from it in some spin chain models. In recent years, entanglement entropy, entanglement spectrum and other measures of correlation have been applied to characterize topological phases of matter, topological phase transitions, and quantum phase transitions within or beyond equilibrium situations. In this collection, we aim to bring together conventional and emerging new topics in the study of entanglement entropy and phase transitions in and out of equilibrium in closed and open quantum systems. Submissions that are related to but not restricted to the following topics are most welcome. We welcome the submission of original research articles, review articles and perspectives.

  • Entanglement in quantum spin chains;
  • Entanglement in topological matter;
  • Entanglement in Floquet systems;
  • Entanglement in non-Hermitian systems;
  • Entanglement in quantum chaotic systems;
  • Entanglement in strongly correlated systems;
  • Entanglement and dynamical quantum phase transitions;
  • Entanglement and ergodicity breaking;
  • Entanglement and localization transitions;
  • Entanglement and measurement-induced phase transitions;
  • Entanglement and quantum computing;
  • Entanglement dynamics;
  • Measures of quantum correlations beyond entanglement;
  • Multipartite entanglement in quantum phase transitions;
  • Detection of entanglement entropy and spectrum.

Prof. Dr. Longwen Zhou
Prof. Dr. Dajian Zhang
Guest Editors

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • entanglement entropy
  • entanglement spectrum
  • entanglement dynamics
  • entanglement transition
  • quantum phase transition
  • topological phases of matter
  • quantum spin chain
  • non-Hermitian systems
  • Floquet systems
  • localization and quantum chaos

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Published Papers (5 papers)

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Research

16 pages, 1467 KiB  
Article
Quantum Phase Transition in the Coupled-Top Model: From Z2 to U(1) Symmetry Breaking
by Wen-Jian Mao, Tian Ye, Liwei Duan and Yan-Zhi Wang
Entropy 2025, 27(5), 474; https://doi.org/10.3390/e27050474 - 27 Apr 2025
Viewed by 266
Abstract
We investigate the coupled-top model, which describes two large spins interacting along both x and y directions. By tuning coupling strengths along distinct directions, the system exhibits different symmetries, ranging from a discrete Z2 to a continuous U(1) symmetry. The anisotropic coupled-top [...] Read more.
We investigate the coupled-top model, which describes two large spins interacting along both x and y directions. By tuning coupling strengths along distinct directions, the system exhibits different symmetries, ranging from a discrete Z2 to a continuous U(1) symmetry. The anisotropic coupled-top model displays a discrete Z2 symmetry, and the symmetry breaking induced by strong coupling drives a quantum phase transition from a disordered paramagnetic phase to an ordered ferromagnetic or antiferromagnetic phase. In particular, the isotropic coupled-top model possesses a continuous U(1) symmetry, whose breaking gives rise to the Goldstone mode. The phase boundary can be well captured by the mean-field approach, characterized by the distinct behaviors of the order parameter. Higher-order quantum effects beyond the mean-field contribution can be achieved by mapping the large spins to bosonic operators via the Holstein–Primakoff transformation. For the anisotropic coupled-top model with Z2 symmetry, the energy gap closes, and both quantum fluctuations and entanglement entropy diverge near the critical point, signaling the onset of second-order quantum phase transitions. Strikingly, when U(1) symmetry is broken, the energy gap vanishes beyond the critical point, yielding a novel critical exponent of 1, rather than 1/2 for Z2 symmetry breaking. The rich symmetry structure of the coupled-top model underpins its role as a paradigmatic model for studying quantum phase transitions and exploring associated physical phenomena. Full article
(This article belongs to the Special Issue Entanglement Entropy and Quantum Phase Transition)
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11 pages, 1003 KiB  
Article
Emergence of Classical Random Walk from Non-Hermitian Effects in Quantum Kicked Rotor
by Wenxuan Song, Jiaming Zhang, Lihao Hua, Zhihua Xiong and Wenlei Zhao
Entropy 2025, 27(3), 288; https://doi.org/10.3390/e27030288 - 10 Mar 2025
Viewed by 536
Abstract
We investigate the quantum random walk in momentum space of a spinor kicked rotor with a non-Hermitian kicking potential. We find that the variance in momentum distributions transitions from quadratic to linear growth over time for the non-Hermitian case. Correspondingly, the momentum distributions [...] Read more.
We investigate the quantum random walk in momentum space of a spinor kicked rotor with a non-Hermitian kicking potential. We find that the variance in momentum distributions transitions from quadratic to linear growth over time for the non-Hermitian case. Correspondingly, the momentum distributions are in the shape of Gaussian wavepackets, providing clear evidence of a classical random walk induced by the non-Hermitian-driven potential. Remarkably, the rate of the linear growth of the variance diverges as the non-Hermitian parameter approaches zero. In the Hermitian case, deviations from the quantum resonance condition dramatically suppress the quadratic growth of the variance, leading to dynamical localization of the quantum walk. Under such quantum non-resonance conditions, the classical random walk is significantly reduced by the non-Hermitian-driven potential. Interestingly, non-Hermiticity enhances quantum entanglement between internal degrees of freedom, while deviations from the quantum resonance condition reduce it. Possible applications of our findings are discussed. Full article
(This article belongs to the Special Issue Entanglement Entropy and Quantum Phase Transition)
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18 pages, 7149 KiB  
Article
Entanglement Phase Transitions in Non-Hermitian Kitaev Chains
by Longwen Zhou
Entropy 2024, 26(3), 272; https://doi.org/10.3390/e26030272 - 20 Mar 2024
Cited by 3 | Viewed by 2082
Abstract
The intricate interplay between unitary evolution and projective measurements could induce entanglement phase transitions in the nonequilibrium dynamics of quantum many-particle systems. In this work, we uncover loss-induced entanglement transitions in non-Hermitian topological superconductors. In prototypical Kitaev chains with onsite particle losses and [...] Read more.
The intricate interplay between unitary evolution and projective measurements could induce entanglement phase transitions in the nonequilibrium dynamics of quantum many-particle systems. In this work, we uncover loss-induced entanglement transitions in non-Hermitian topological superconductors. In prototypical Kitaev chains with onsite particle losses and varying hopping and pairing ranges, the bipartite entanglement entropy of steady states is found to scale logarithmically versus the system size in topologically nontrivial phases and become independent of the system size in the trivial phase. Notably, the scaling coefficients of log-law entangled phases are distinguishable when the underlying system resides in different topological phases. Log-law to log-law and log-law to area-law entanglement phase transitions are further identified when the system switches between different topological phases and goes from a topologically nontrivial to a trivial phase, respectively. These findings not only establish the relationships among spectral, topological and entanglement properties in a class of non-Hermitian topological superconductors but also provide an efficient means to dynamically reveal their distinctive topological features. Full article
(This article belongs to the Special Issue Entanglement Entropy and Quantum Phase Transition)
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10 pages, 365 KiB  
Article
Quadratic Growth of Out-of-Time-Ordered Correlators in Quantum Kicked Rotor Model
by Guanling Li and Wenlei Zhao
Entropy 2024, 26(3), 229; https://doi.org/10.3390/e26030229 - 3 Mar 2024
Cited by 1 | Viewed by 1686
Abstract
We investigate both theoretically and numerically the dynamics of out-of-time-ordered correlators (OTOCs) in quantum resonance conditions for a kicked rotor model. We employ various operators to construct OTOCs in order to thoroughly quantify their commutation relation at different times, therefore unveiling the process [...] Read more.
We investigate both theoretically and numerically the dynamics of out-of-time-ordered correlators (OTOCs) in quantum resonance conditions for a kicked rotor model. We employ various operators to construct OTOCs in order to thoroughly quantify their commutation relation at different times, therefore unveiling the process of quantum scrambling. With the help of quantum resonance condition, we have deduced the exact expressions of quantum states during both forward evolution and time reversal, which enables us to establish the laws governing OTOCs’ time dependence. We find interestingly that the OTOCs of different types increase in a quadratic function of time, breaking the freezing of quantum scrambling induced by the dynamical localization under non-resonance condition. The underlying mechanism is discovered, and the possible applications in quantum entanglement are discussed. Full article
(This article belongs to the Special Issue Entanglement Entropy and Quantum Phase Transition)
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11 pages, 2235 KiB  
Article
Mutual Information and Correlations across Topological Phase Transitions in Topologically Ordered Graphene Zigzag Nanoribbons
by In-Hwan Lee, Hoang-Anh Le and S.-R. Eric Yang
Entropy 2023, 25(10), 1449; https://doi.org/10.3390/e25101449 - 15 Oct 2023
Cited by 3 | Viewed by 1823
Abstract
Graphene zigzag nanoribbons, initially in a topologically ordered state, undergo a topological phase transition into crossover phases distinguished by quasi-topological order. We computed mutual information for both the topologically ordered phase and its crossover phases, revealing the following results: (i) In the topologically [...] Read more.
Graphene zigzag nanoribbons, initially in a topologically ordered state, undergo a topological phase transition into crossover phases distinguished by quasi-topological order. We computed mutual information for both the topologically ordered phase and its crossover phases, revealing the following results: (i) In the topologically ordered phase, A-chirality carbon lines strongly entangle with B-chirality carbon lines on the opposite side of the zigzag ribbon. This entanglement persists but weakens in crossover phases. (ii) The upper zigzag edge entangles with non-edge lines of different chirality on the opposite side of the ribbon. (iii) Entanglement increases as more carbon lines are grouped together, regardless of the lines’ chirality. No long-range entanglement was found in the symmetry-protected phase in the absence of disorder. Full article
(This article belongs to the Special Issue Entanglement Entropy and Quantum Phase Transition)
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