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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: 15 July 2024 | Viewed by 3628

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

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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

Published Papers (3 papers)

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Research

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
Viewed by 708
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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9 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 - 03 Mar 2024
Viewed by 856
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 1 | Viewed by 1037
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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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Tentative title: Entropy Generated by Flat Band

Authors: V.R. Shaginyan 1,2, A.Z. Msezane 1, and S.A. Artamonov 2

Affiliations:

1. Petersburg Nuclear Physics Institute of NRC ”Kurchatov Institute”, Gatchina, 188300, Russia

2. Clark Atlanta University, Atlanta, GA 30314, USA

Abstract:

In our review, we consider the relationships between the entropy and the corresponding flat band that forms the properties of heavy fermion compounds. We show that on one hand, that the entropy stabilizes flat band. On the other hand, the entropy promotes a variety of phase transitions in the vicinity of quantum phase transition, generating the flat band. We analyze the influence of temperature, magnetic field, pressure, superconductivity, etc on the distortion of flat band and the corresponding entropy. We also reveal how the entropy forms such special properties of heavy fermion compounds as the asymmetrical differential conductivity, particle – hole asymmetry, additional residual resistivity and etc.

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