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Zamani S, Naji J, Jafari R, Langari A. Scaling and universality at ramped quench dynamical quantum phase transitions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:355401. [PMID: 38768603 DOI: 10.1088/1361-648x/ad4df9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Accepted: 05/20/2024] [Indexed: 05/22/2024]
Abstract
The nonequilibrium dynamics of a periodically driven extended XY model, in the presence of linear time dependent magnetic field, is investigated using the notion of dynamical quantum phase transitions (DQPTs). Along the similar lines to the equilibrium phase transition, the main purpose of this work is to search fundamental concepts such as scaling and universality at the ramped quench DQPTs. We have shown that the critical points of the model, where the gap closing occurs, can be moved by tuning the driven frequency and consequently the presence of or absence of DQPTs can be flexibly controlled by adjusting the driven frequency. We have uncovered that, for a ramp across the single quantum critical point, the critical mode at which DQPTs occur is classified into three regions: the Kibble-Zurek (KZ) region, where the critical mode scales linearly with the square root of the sweep velocity, the pre-saturated (PS) region, and the saturated (S) region where the critical mode makes a plateau versus the sweep velocity. While for a ramp that crosses two critical points, the critical modes disclose just the KZ and PS regions. On the basis of numerical simulations, we find that the dynamical free energy scales linearly with time, as approaches to DQPT time, with the exponentν=1±0.01for all sweep velocities and driven frequencies.
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Affiliation(s)
- Sara Zamani
- Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
| | - J Naji
- Department of Physics, Faculty of Science, Ilam University, Ilam, Iran
| | - R Jafari
- Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
- School of Nano Science, Institute for Research in Fundamental Sciences (IPM), 19395-5531 Tehran, Iran
- Department of Physics, University of Gothenburg, SE 412 96 Gothenburg, Sweden
| | - A Langari
- Department of Physics, Sharif University of Technology, 11155-9161 Tehran, Iran
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Masłowski T, Sedlmayr N. The dynamical bulk boundary correspondence and dynamical quantum phase transitions in the Benalcazar-Bernevig-Hughes model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:335401. [PMID: 38729200 DOI: 10.1088/1361-648x/ad4a16] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2024] [Accepted: 05/10/2024] [Indexed: 05/12/2024]
Abstract
In this article we demonstrate that dynamical quantum phase transitions (DQPTs) occur for an exemplary higher order topological insulator, the Benalcazar-Bernevig-Hughes model, following quenches across a topological phase boundary. A dynamical bulk boundary correspondence is also seen both in the eigenvalues of the Loschmidt overlap matrix and the boundary return rate. The latter is found from a finite size scaling analysis for which the relative simplicity of the model is crucial. Contrary to the usual two dimensional case the DQPTs in this model show up as cusps in the return rate, as for a one dimensional model, rather than as cusps in its derivative as would be typical for a two dimensional model. We explain the origin of this behaviour.
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Affiliation(s)
- Tomasz Masłowski
- The Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, al. Powstańców Warszawy 6, 35-959 Rzeszów, Poland
| | - Nicholas Sedlmayr
- Institute of Physics, M. Curie-Skłodowska University, 20-031 Lublin, Poland
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Corps ÁL, Relaño A. Theory of Dynamical Phase Transitions in Quantum Systems with Symmetry-Breaking Eigenstates. PHYSICAL REVIEW LETTERS 2023; 130:100402. [PMID: 36962016 DOI: 10.1103/physrevlett.130.100402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Revised: 10/03/2022] [Accepted: 02/16/2023] [Indexed: 06/18/2023]
Abstract
We present a theory for the two kinds of dynamical quantum phase transitions, termed DPT-I and DPT-II, based on a minimal set of symmetry assumptions. In the special case of collective systems with infinite-range interactions, both are triggered by excited-state quantum phase transitions. For quenches below the critical energy, the existence of an additional conserved charge, identifying the corresponding phase, allows for a nonzero value of the dynamical order parameter characterizing DPTs-I, and precludes the main mechanism giving rise to nonanalyticities in the return probability, trademark of DPTs-II. We propose a statistical ensemble describing the long-time averages of order parameters in DPTs-I, and provide a theoretical proof for the incompatibility of the main mechanism for DPTs-II with the presence of this additional conserved charge. Our results are numerically illustrated in the fully connected transverse-field Ising model, which exhibits both kinds of dynamical phase transitions. Finally, we discuss the applicability of our theory to systems with finite-range interactions, where the phenomenology of excited-state quantum phase transitions is absent. We illustrate our findings by means of numerical calculations with experimentally relevant initial states.
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Affiliation(s)
- Ángel L Corps
- Instituto de Estructura de la Materia, IEM-CSIC, Serrano 123, E-28006 Madrid, Spain
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Complutense de Madrid, Avenida Complutense s/n, E-28040 Madrid, Spain
| | - Armando Relaño
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Complutense de Madrid, Avenida Complutense s/n, E-28040 Madrid, Spain
- Departamento de Estructura de la Materia, Física Térmica y Electrónica, Universidad Complutense de Madrid, Avenida Complutense s/n, E-28040 Madrid, Spain
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Li X, Ma Y, Wang D, Wang Y, Zhao S. Reconstructing the dynamical quantum phase transitions via dimensional expansion in a generalized Su-Schrieffer-Heeger model. Phys Rev E 2022; 106:014124. [PMID: 35974531 DOI: 10.1103/physreve.106.014124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2021] [Accepted: 06/23/2022] [Indexed: 06/15/2023]
Abstract
We know that a one-dimensional (1D) modulated system can simulate 2D topological states by expanding the dimension. This scenario provides a justifiable avenue to test the dilatation of the dynamical quantum phase transition (DQPT). Through a generalized Su-Schrieffer-Heeger model, we have shown how the Loschmidt echo, Fisher zero, and Dynamical topological order parameter (DTOP) transit from one to two dimensions. Owing to the introduced pseudomomentum, the derivative of the return rate does not always capture the DQPT well, but the Fisher zero and the DTOP can be treated as faithful indicators. A topology-independent parameter will also affect the occurrence of the DQPTs for quenches inside a given phase. Moreover, a comparison with the Haldane model owning the same phase diagram implies that a pair of fixed points will lead to different critical momentum distributions, thus different robustness, further reminding us that the correspondences between the equilibrium and dynamical phases transitions are multifarious.
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Affiliation(s)
- Xin Li
- Data Science Research Center, Kunming University of Science and Technology, Kunming 650093, China
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - YuXuan Ma
- Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China
| | - DuoJia Wang
- Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China
| | - Yu Wang
- Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China
| | - ShunCai Zhao
- Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China
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Dolgitzer D, Zeng D, Chen Y. Dynamical quantum phase transitions in the spin-boson model. OPTICS EXPRESS 2021; 29:23988-23996. [PMID: 34614652 DOI: 10.1364/oe.434183] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 07/05/2021] [Indexed: 06/13/2023]
Abstract
We study dynamical quantum phase transitions in a 2-qubit system interacting with a transverse field and a quantized bosonic environment in the context of open quantum systems. By applying the stochastic Schrödinger equation approach, the model with a spin-boson type of coupling can be solved numerically. It is observed that the dynamics of the rate function of the Loschmidt echo in a 2-qubit system within a finite size of Hilbert space exhibit nonanalyticity when the direction of the transverse field coupled to the system is under a sudden quench. Moreover, we demonstrate that the memory time of the environment and the coupling strength between the system and the transverse field can jointly impact the dynamics of the rate function. We also supply a semi-classical explanation to bridge the dynamical quantum phase transitions in many-body systems and the non-Markovian dynamics of open quantum systems.
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Zhou L, Du Q. Floquet dynamical quantum phase transitions in periodically quenched systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:345403. [PMID: 34130264 DOI: 10.1088/1361-648x/ac0b60] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2021] [Accepted: 06/15/2021] [Indexed: 06/12/2023]
Abstract
Dynamical quantum phase transitions (DQPTs) are characterized by nonanalytic behaviors of physical observables as functions of time. When a system is subject to time-periodic modulations, the nonanalytic signatures of its observables could recur periodically in time, leading to the phenomena of Floquet DQPTs. In this work, we systematically explore Floquet DQPTs in a class of periodically quenched one-dimensional system with chiral symmetry. By tuning the strength of quench, we find multiple Floquet DQPTs within a single driving period, with more DQPTs being observed when the system is initialized in Floquet states with larger topological invariants. Each Floquet DQPT is further accompanied by the quantized jump of a dynamical topological order parameter, whose values remain quantized in time if the underlying Floquet system is prepared in a gapped topological phase. The theory is demonstrated in a piecewise quenched lattice model, which possesses rich Floquet topological phases and is readily realizable in quantum simulators like the nitrogen-vacancy center in diamonds. Our discoveries thus open a new perspective for the Floquet engineering of DQPTs and the dynamical detection of topological phase transitions in Floquet systems.
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Affiliation(s)
- Longwen Zhou
- Department of Physics, College of Information Science and Engineering, Ocean University of China, Qingdao, 266100, People's Republic of China
| | - Qianqian Du
- Department of Physics, College of Information Science and Engineering, Ocean University of China, Qingdao, 266100, People's Republic of China
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Mzaouali Z, Puebla R, Goold J, El Baz M, Campbell S. Work statistics and symmetry breaking in an excited-state quantum phase transition. Phys Rev E 2021; 103:032145. [PMID: 33862795 DOI: 10.1103/physreve.103.032145] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Accepted: 03/02/2021] [Indexed: 11/07/2022]
Abstract
We examine how the presence of an excited-state quantum phase transition manifests in the dynamics of a many-body system subject to a sudden quench. Focusing on the Lipkin-Meshkov-Glick model initialized in the ground state of the ferromagnetic phase, we demonstrate that the work probability distribution displays non-Gaussian behavior for quenches in the vicinity of the excited-state critical point. Furthermore, we show that the entropy of the diagonal ensemble is highly susceptible to critical regions, making it a robust and practical indicator of the associated spectral characteristics. We assess the role that symmetry breaking has on the ensuing dynamics, highlighting that its effect is only present for quenches beyond the critical point. Finally, we show that similar features persist when the system is initialized in an excited state and briefly explore the behavior for initial states in the paramagnetic phase.
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Affiliation(s)
- Zakaria Mzaouali
- ESMaR, Faculty of Sciences, Mohammed V University in Rabat, Morocco
| | - Ricardo Puebla
- Instituto de Física Fundamental, IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain.,Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - John Goold
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
| | - Morad El Baz
- ESMaR, Faculty of Sciences, Mohammed V University in Rabat, Morocco
| | - Steve Campbell
- School of Physics, University College Dublin, Belfield, Dublin 4, Ireland.,Centre for Quantum Engineering, Science, and Technology, University College Dublin, Belfield, Dublin 4, Ireland
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De Nicola S, Michailidis AA, Serbyn M. Entanglement View of Dynamical Quantum Phase Transitions. PHYSICAL REVIEW LETTERS 2021; 126:040602. [PMID: 33576663 DOI: 10.1103/physrevlett.126.040602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2020] [Accepted: 12/23/2020] [Indexed: 06/12/2023]
Abstract
The analogy between an equilibrium partition function and the return probability in many-body unitary dynamics has led to the concept of dynamical quantum phase transition (DQPT). DQPTs are defined by nonanalyticities in the return amplitude and are present in many models. In some cases, DQPTs can be related to equilibrium concepts, such as order parameters, yet their universal description is an open question. In this Letter, we provide first steps toward a classification of DQPTs by using a matrix product state description of unitary dynamics in the thermodynamic limit. This allows us to distinguish the two limiting cases of "precession" and "entanglement" DQPTs, which are illustrated using an analytical description in the quantum Ising model. While precession DQPTs are characterized by a large entanglement gap and are semiclassical in their nature, entanglement DQPTs occur near avoided crossings in the entanglement spectrum and can be distinguished by a complex pattern of nonlocal correlations. We demonstrate the existence of precession and entanglement DQPTs beyond Ising models, discuss observables that can distinguish them, and relate their interplay to complex DQPT phenomenology.
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Affiliation(s)
| | | | - Maksym Serbyn
- IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
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