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Current Trends in Quantum Phase Transitions
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Current Trends in Quantum Phase Transitions

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

Deadline for manuscript submissions: closed (15 June 2022) | Viewed by 14968

Special Issue Editor

Dr. Miguel A. Bastarrachea-Magnani

E-Mail Website
Guest Editor
Department of Physics, Universidad Autónoma Metropolitana-Iztapalapa, Ciudad de México 09340, Mexico
Interests: light–matter interaction; exciton–polariton; quantum phase transitions; quantum chaos
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

During the last three decades the study of Quantum Phase Transitions (QPTs) has been under continuous development and has become a mature and well-established field. Identified as sudden changes in the ground-state properties of quantum systems as their parameters change, QPTs occur in a wide range of different systems, from atomic physics and quantum optics to condensed matter. As a consequence, their research has contributed to the establishment of connections across several fields of physics and to the unraveling of new features in both few- and many-body quantum problems.

Thanks to the progress on new experimental, theoretical and numerical tools, the concept of QPT has recently been extended to other domains including excited states and nonequilibrium setups, where the understanding of critical phenomena such as excited-state quantum phase transitions and dynamical phase transitions still poses challenges. Unquestionably, the field is a fruitful one and several questions remain open about the relationship between quantum critical phenomena and topics such as chaos, entanglement, localization, transport, thermal effects, finite-size effects as well as their role in out-of-equilibrium processes and the quantum-classical correspondence, among several others. This Special Issue aims to review recent trends in the study of quantum phase transitions, covering, but not restricted to, the following areas:

*) quantum phase transitions in novel systems;

*) excited-state quantum phase transitions (ESQPTs);

*) dynamical quantum phase transitions (DPTs);

*) transport and dynamic properties in the quantum critical region;

*) chaos, localization and quantum criticality.

Dr. Miguel A. Bastarrachea-Magnani
Guest Editor

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

  • Quantum phase transitions
  • Excited-state quantum phase transitions
  • Dynamical phase transitions
  • Critical phenomena
  • Nonequilibrium processes
  • Phase diagrams
  • Finite-size effects

Published Papers (7 papers)

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Research

34 pages, 26000 KiB  
Article
Critical Phenomena in Light–Matter Systems with Collective Matter Interactions
by Ricardo Herrera Romero, Miguel Angel Bastarrachea-Magnani and Román Linares
Entropy 2022, 24(9), 1198; https://doi.org/10.3390/e24091198 - 27 Aug 2022
Cited by 3 | Viewed by 1642
Abstract
We study the quantum phase diagram and the onset of quantum critical phenomena in a generalized Dicke model that includes collective qubit–qubit interactions. By employing semiclassical techniques, we analyze the corresponding classical energy surfaces, fixed points, and the smooth Density of States as [...] Read more.
We study the quantum phase diagram and the onset of quantum critical phenomena in a generalized Dicke model that includes collective qubit–qubit interactions. By employing semiclassical techniques, we analyze the corresponding classical energy surfaces, fixed points, and the smooth Density of States as a function of the Hamiltonian parameters to determine quantum phase transitions in either the ground (QPT) or excited states (ESQPT). We unveil a rich phase diagram, the presence of new phases, and new transitions that result from varying the strength of the qubits interactions in independent canonical directions. We also find a correspondence between the phases emerging due to qubit interactions and those in their absence but with varying the strength of the non-resonant terms in the light–matter coupling. We expect our work to pave the way and stimulate the exploration of quantum criticality in systems combining matter–matter and light–matter interactions. Full article
(This article belongs to the Special Issue Current Trends in Quantum Phase Transitions)
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11 pages, 4222 KiB  
Article
Critical Quantum Metrology in the Non-Linear Quantum Rabi Model
by Zu-Jian Ying, Simone Felicetti, Gang Liu and Daniel Braak
Entropy 2022, 24(8), 1015; https://doi.org/10.3390/e24081015 - 22 Jul 2022
Cited by 19 | Viewed by 2080
Abstract
The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear [...] Read more.
The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms. Full article
(This article belongs to the Special Issue Current Trends in Quantum Phase Transitions)
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14 pages, 671 KiB  
Article
Kibble–Zurek Scaling from Linear Response Theory
by Pierre Nazé, Marcus V. S. Bonança and Sebastian Deffner
Entropy 2022, 24(5), 666; https://doi.org/10.3390/e24050666 - 10 May 2022
Cited by 7 | Viewed by 2013
Abstract
While quantum phase transitions share many characteristics with thermodynamic phase transitions, they are also markedly different as they occur at zero temperature. Hence, it is not immediately clear whether tools and frameworks that capture the properties of thermodynamic phase transitions also apply in [...] Read more.
While quantum phase transitions share many characteristics with thermodynamic phase transitions, they are also markedly different as they occur at zero temperature. Hence, it is not immediately clear whether tools and frameworks that capture the properties of thermodynamic phase transitions also apply in the quantum case. Concerning the crossing of thermodynamic critical points and describing its non-equilibrium dynamics, the Kibble–Zurek mechanism and linear response theory have been demonstrated to be among the very successful approaches. In the present work, we show that these two approaches are also consistent in the description of quantum phase transitions, and that linear response theory can even inform arguments of the Kibble–Zurek mechanism. In particular, we show that the relaxation time provided by linear response theory gives a rigorous argument for why to identify the “gap” as a relaxation rate, and we verify that the excess work computed from linear response theory exhibits Kibble–Zurek scaling. Full article
(This article belongs to the Special Issue Current Trends in Quantum Phase Transitions)
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12 pages, 555 KiB  
Article
The Classical–Quantum Passage: A van der Waals Description
by Flavia Pennini and Angel Plastino
Entropy 2022, 24(2), 182; https://doi.org/10.3390/e24020182 - 26 Jan 2022
Cited by 1 | Viewed by 1693
Abstract
We undertake a van der Waals inquiry at very low temperatures so as to find signs of a classical–quantum frontier. We investigate the relation of such signs with the celebrated van der Waals gas–liquid transition. We specialize the discussion with respect to the [...] Read more.
We undertake a van der Waals inquiry at very low temperatures so as to find signs of a classical–quantum frontier. We investigate the relation of such signs with the celebrated van der Waals gas–liquid transition. We specialize the discussion with respect to the noble gases. For such purpose, we use rather novel thermal statistical quantifiers such as the disequilibrium, the statistical complexity, and the thermal efficiency. Fruitful insights are thereby gained. Full article
(This article belongs to the Special Issue Current Trends in Quantum Phase Transitions)
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16 pages, 379 KiB  
Article
Entropies and IPR as Markers for a Phase Transition in a Two-Level Model for Atom–Diatomic Molecule Coexistence
by Ignacio Baena, Pedro Pérez-Fernández, Manuela Rodríguez-Gallardo and José Miguel Arias
Entropy 2022, 24(1), 113; https://doi.org/10.3390/e24010113 - 12 Jan 2022
Cited by 2 | Viewed by 1497
Abstract
A quantum phase transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, which is briefly discussed, presents a second-order ground state phase transition in the thermodynamic (or large particle number) limit, changing from [...] Read more.
A quantum phase transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, which is briefly discussed, presents a second-order ground state phase transition in the thermodynamic (or large particle number) limit, changing from a molecular condensate in one phase to an equilibrium of diatomic molecules–atoms in coexistence in the other one. The usual markers for this phase transition are the ground state energy and the expected value of the number of atoms (alternatively, the number of molecules) in the ground state. In this work, other markers for the QPT, such as the inverse participation ratio (IPR), and particularly, the Rényi entropy, are analyzed and proposed as QPT markers. Both magnitudes present abrupt changes at the critical point of the QPT. Full article
(This article belongs to the Special Issue Current Trends in Quantum Phase Transitions)
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14 pages, 911 KiB  
Article
Ground State, Magnetization Process and Bipartite Quantum Entanglement of a Spin-1/2 Ising–Heisenberg Model on Planar Lattices of Interconnected Trigonal Bipyramids
by Lucia Gálisová and Michał Kaczor
Entropy 2021, 23(12), 1671; https://doi.org/10.3390/e23121671 - 12 Dec 2021
Cited by 4 | Viewed by 2244
Abstract
The ground state, magnetization scenario and the local bipartite quantum entanglement of a mixed spin-1/2 Ising–Heisenberg model in a magnetic field on planar lattices formed by identical corner-sharing bipyramidal plaquettes is examined by combining the exact analytical concept of generalized [...] Read more.
The ground state, magnetization scenario and the local bipartite quantum entanglement of a mixed spin-1/2 Ising–Heisenberg model in a magnetic field on planar lattices formed by identical corner-sharing bipyramidal plaquettes is examined by combining the exact analytical concept of generalized decoration-iteration mapping transformations with Monte Carlo simulations utilizing the Metropolis algorithm. The ground-state phase diagram of the model involves six different phases, namely, the standard ferrimagnetic phase, fully saturated phase, two unique quantum ferrimagnetic phases, and two macroscopically degenerate quantum ferrimagnetic phases with two chiral degrees of freedom of the Heisenberg triangular clusters. The diversity of ground-state spin arrangement is manifested themselves in seven different magnetization scenarios with one, two or three fractional plateaus whose values are determined by the number of corner-sharing plaquettes. The low-temperature values of the concurrence demonstrate that the bipartite quantum entanglement of the Heisenberg spins in quantum ferrimagnetic phases is field independent, but twice as strong if the Heisenberg spin arrangement is unique as it is two-fold degenerate. Full article
(This article belongs to the Special Issue Current Trends in Quantum Phase Transitions)
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19 pages, 3193 KiB  
Article
Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos
by Qian Wang and Marko Robnik
Entropy 2021, 23(10), 1347; https://doi.org/10.3390/e23101347 - 15 Oct 2021
Cited by 11 | Viewed by 2272
Abstract
We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical [...] Read more.
We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos. Full article
(This article belongs to the Special Issue Current Trends in Quantum Phase Transitions)
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