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Herrera Romero R, Bastarrachea-Magnani MA. Phase and Amplitude Modes in the Anisotropic Dicke Model with Matter Interactions. ENTROPY (BASEL, SWITZERLAND) 2024; 26:574. [PMID: 39056936 PMCID: PMC11276390 DOI: 10.3390/e26070574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2024] [Revised: 06/29/2024] [Accepted: 07/01/2024] [Indexed: 07/28/2024]
Abstract
Phase and amplitude modes, also called polariton modes, are emergent phenomena that manifest across diverse physical systems, from condensed matter and particle physics to quantum optics. We study their behavior in an anisotropic Dicke model that includes collective matter interactions. We study the low-lying spectrum in the thermodynamic limit via the Holstein-Primakoff transformation and contrast the results with the semi-classical energy surface obtained via coherent states. We also explore the geometric phase for both boson and spin contours in the parameter space as a function of the phases in the system. We unveil novel phenomena due to the unique critical features provided by the interplay between the anisotropy and matter interactions. We expect our results to serve the observation of phase and amplitude modes in current quantum information platforms.
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Affiliation(s)
| | - Miguel Angel Bastarrachea-Magnani
- Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Av. Ferrocarril San Rafael Atlixco 186, Mexico City C.P. 09310, Mexico
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Merici TA, De Mattos TG, Peixoto De Faria JG. Degeneracy and Photon Trapping in a Dissipationless Two-Mode Optomechanical Model. ENTROPY (BASEL, SWITZERLAND) 2024; 26:87. [PMID: 38275495 PMCID: PMC10813945 DOI: 10.3390/e26010087] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2023] [Revised: 01/09/2024] [Accepted: 01/12/2024] [Indexed: 01/27/2024]
Abstract
In this work, we theoretically study a finite and undamped two-mode optomechanical model consisting of a high quality optical cavity containing a thin, elastic, and dielectric membrane. The main objective is to investigate the precursors of quantum phase transition in such a model by studying the behavior of some observables in the ground state. By controlling the coupling between membrane and modes, we find that the two lowest energy eigenstates become degenerate, as is indicated by the behavior of the mean value of some operators and by other quantifiers as a function of the coupling. Such degenerate states are characterized by a coherent superposition of eigenstates describing one of the two modes preferentially populated and the membrane dislocated from its equilibrium position due the radiation pressure (Schrödinger's cat states). The delocalization of the compound system photons+membrane results in an increase in fluctuations as measured by Robertson-Schrödinger uncertainty relations.
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Affiliation(s)
- Thiago Alonso Merici
- Programa de Pós-Graduação em Modelagem Matemática e Computacional, Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG), Av. Amazonas 7675, Belo Horizonte 30510-000, MG, Brazil; (T.A.M.); (T.G.D.M.)
| | - Thiago Gomes De Mattos
- Programa de Pós-Graduação em Modelagem Matemática e Computacional, Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG), Av. Amazonas 7675, Belo Horizonte 30510-000, MG, Brazil; (T.A.M.); (T.G.D.M.)
- Departamento de Física, Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG), Av. Amazonas 7675, Belo Horizonte 30510-000, MG, Brazil
| | - José Geraldo Peixoto De Faria
- Programa de Pós-Graduação em Modelagem Matemática e Computacional, Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG), Av. Amazonas 7675, Belo Horizonte 30510-000, MG, Brazil; (T.A.M.); (T.G.D.M.)
- Departamento de Matemática, Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG), Av. Amazonas 7675, Belo Horizonte 30510-000, MG, Brazil
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Khalouf-Rivera J, Gamito J, Pérez-Bernal F, Arias JM, Pérez-Fernández P. Excited-state quantum phase transitions in the anharmonic Lipkin-Meshkov-Glick model: Dynamical aspects. Phys Rev E 2023; 107:064134. [PMID: 37464676 DOI: 10.1103/physreve.107.064134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 06/07/2023] [Indexed: 07/20/2023]
Abstract
The standard Lipkin-Meshkov-Glick (LMG) model undergoes a second-order ground-state quantum phase transition (QPT) and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the LMG Hamiltonian gives rise to a second ESQPT that alters the static properties of the model [Gamito et al., Phys. Rev. E 106, 044125 (2022)2470-004510.1103/PhysRevE.106.044125]. In the present work, the dynamical implications associated to this new ESQPT are analyzed. For that purpose, a quantum quench protocol is defined on the system Hamiltonian that takes an initial state, usually the ground state, into a complex excited state that evolves on time. The impact of the new ESQPT on the time evolution of the survival probability and the local density of states after the quantum quench, as well as on the Loschmidt echoes and the microcanonical out-of-time-order correlator (OTOC) are discussed. The anharmonity-induced ESQPT, despite having a different physical origin, has dynamical consequences similar to those observed in the ESQPT already present in the standard LMG model.
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Affiliation(s)
- J Khalouf-Rivera
- Departamento de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
| | - J Gamito
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain
| | - F Pérez-Bernal
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
| | - J M Arias
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
| | - P Pérez-Fernández
- Departamento de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
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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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5
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Convergence of Møller–Plesset perturbation theory for excited reference states. ADVANCES IN QUANTUM CHEMISTRY 2023. [DOI: 10.1016/bs.aiq.2023.01.012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/16/2023]
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Gamito J, Khalouf-Rivera J, Arias JM, Pérez-Fernández P, Pérez-Bernal F. Excited-state quantum phase transitions in the anharmonic Lipkin-Meshkov-Glick model: Static aspects. Phys Rev E 2022; 106:044125. [PMID: 36397542 DOI: 10.1103/physreve.106.044125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Accepted: 08/15/2022] [Indexed: 06/16/2023]
Abstract
The basic Lipkin-Meshkov-Glick model displays a second-order ground-state quantum phase transition and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the Hamiltonian implies a second ESQPT of a different nature. We characterize this ESQPT using the mean field limit of the model. The alternative ESQPT, associated with the changes in the boundary of the finite Hilbert space of the system, can be properly described using the order parameter of the ground-state quantum phase transition, the energy gap between adjacent states, the participation ratio, and the quantum fidelity susceptibility.
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Affiliation(s)
- J Gamito
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, 41080 Sevilla, Spain
| | - J Khalouf-Rivera
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
| | - J M Arias
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, 41080 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
| | - P Pérez-Fernández
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
- Departamento de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain
| | - F Pérez-Bernal
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
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Herrera Romero R, Bastarrachea-Magnani MA, Linares R. Critical Phenomena in Light-Matter Systems with Collective Matter Interactions. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1198. [PMID: 36141084 PMCID: PMC9497676 DOI: 10.3390/e24091198] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Revised: 08/20/2022] [Accepted: 08/23/2022] [Indexed: 06/16/2023]
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 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.
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8
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Sun Y, Burton HGA. Complex analysis of divergent perturbation theory at finite temperature. J Chem Phys 2022; 156:171101. [DOI: 10.1063/5.0091442] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the convergence properties of finite-temperature perturbation theory by considering the mathematical structure of thermodynamic potentials using complex analysis. We discover that zeros of the partition function lead to poles in the internal energy and logarithmic singularities in the Helmholtz free energy that create divergent expansions in the canonical ensemble. Analyzing these zeros reveals that the radius of convergence increases at higher temperatures. In contrast, when the reference state is degenerate, these poles in the internal energy create a zero radius of convergence in the zero-temperature limit. Finally, by showing that the poles in the internal energy reduce to exceptional points in the zero-temperature limit, we unify the two main mathematical representations of quantum phase transitions.
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Affiliation(s)
- Yi Sun
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Hugh G. A. Burton
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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9
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Stránský P, Dvořák M, Cejnar P. Exceptional points near first- and second-order quantum phase transitions. Phys Rev E 2018; 97:012112. [PMID: 29448346 DOI: 10.1103/physreve.97.012112] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2017] [Indexed: 06/08/2023]
Abstract
We study the impact of quantum phase transitions (QPTs) on the distribution of exceptional points (EPs) of the Hamiltonian in the complex-extended parameter domain. Analyzing first- and second-order QPTs in the Lipkin-Meshkov-Glick model we find an exponentially and polynomially close approach of EPs to the respective critical point with increasing size of the system. If the critical Hamiltonian is subject to random perturbations of various kinds, the averaged distribution of EPs close to the critical point still carries decisive information on the QPT type. We therefore claim that properties of the EP distribution represent a parametrization-independent signature of criticality in quantum systems.
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Affiliation(s)
- Pavel Stránský
- Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00 Prague, Czech Republic
| | - Martin Dvořák
- Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00 Prague, Czech Republic
| | - Pavel Cejnar
- Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00 Prague, Czech Republic
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10
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Frazão HM, de Faria JGP, Pellegrino GQ, Nemes MC. Quantum phase transition in an effective three-mode model of interacting bosons. Phys Rev E 2017; 96:062146. [PMID: 29347450 DOI: 10.1103/physreve.96.062146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2017] [Indexed: 06/07/2023]
Abstract
In this work we study an effective three-mode model describing interacting bosons. These bosons can be considered as exciton-polaritons in a semiconductor microcavity at the magic angle. This model exhibits quantum phase transition (QPT) when the parameters of the corresponding Hamiltonian are continuously varied. The properties of the Hamiltonian spectrum (e.g., the distance between two adjacent energy levels) and the phase space structure of the thermodynamic limit of the model are used to indicate QPT. The relation between spectral properties of the Hamiltonian and the corresponding classical frame of the thermodynamic limit of the model is established as indicative of QPT. The average number of bosons in a specific mode and the entanglement properties of the ground state as functions of the parameters are used to characterize the order of the transition and also to construct a phase diagram. Finally, we verify our results for experimental data obtained for a setting of exciton-polaritons in a semiconductor microcavity.
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Affiliation(s)
- H M Frazão
- Universidade Federal do Piauí, Campus Profa. Cinobelina Elvas, Bom Jesus, PI, Brazil
- Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil
| | - J G Peixoto de Faria
- Departamento de Matemática, Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, MG, Brazil
| | - G Q Pellegrino
- Departamento de Matemática, Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, MG, Brazil
| | - M C Nemes
- Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil
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Castaños O, Calixto M, Pérez-Bernal F, Romera E. Identifying the order of a quantum phase transition by means of Wehrl entropy in phase space. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052106. [PMID: 26651646 DOI: 10.1103/physreve.92.052106] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2015] [Indexed: 06/05/2023]
Abstract
We propose a method to identify the order of a quantum phase transition by using area measures of the ground state in phase space. We illustrate our proposal by analyzing the well known example of the quantum cusp and four different paradigmatic boson models: Dicke, Lipkin-Meshkov-Glick, interacting boson model, and vibron model.
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Affiliation(s)
- Octavio Castaños
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 Distrito Federal, Mexico
| | - Manuel Calixto
- Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
| | - Francisco Pérez-Bernal
- Departamento de Física Aplicada, Facultad de Ciencias Experimentales, Universidad de Huelva, Campus del Carmen, Avenida de las Fuerzas Armadas s/n, 21071 Huelva, Spain
| | - Elvira Romera
- Departamento de Física Atómica, Molecular y Nuclear and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
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12
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Ribeiro P, Vidal J, Mosseri R. Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:021106. [PMID: 18850785 DOI: 10.1103/physreve.78.021106] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2008] [Indexed: 05/26/2023]
Abstract
The spectrum of the Lipkin-Meshkov-Glick model is exactly derived in the thermodynamic limit by means of a spin-coherent-state formalism. In the first step, a classical analysis allows one to distinguish between four distinct regions in the parameter space according to the nature of the singularities arising in the classical energy surface; these correspond to spectral critical points. The eigenfunctions are then analyzed more precisely in terms of the associated roots of the Majorana polynomial, leading to exact expressions for the density of states in the thermodynamic limit. Finite-size effects are also analyzed, leading in particular to logarithmic corrections near the singularities occurring in the spectrum. Finally, we also compute expectation values of the spin operators in a semiclassical analysis in order to illustrate some subtle effects occurring in one region of the parameter space.
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Affiliation(s)
- Pedro Ribeiro
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France.
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13
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Moreira T, Pellegrino GQ, Peixoto de Faria JG, Nemes MC, Camargo F, de Toledo Piza AFR. Entanglement and classical instabilities: fingerprints of electron-hole-to-exciton phase transition in a simple model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:051102. [PMID: 18643021 DOI: 10.1103/physreve.77.051102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2008] [Revised: 03/18/2008] [Indexed: 05/26/2023]
Abstract
We propose a schematic model to study the formation of excitons in bilayer electron systems. The phase transition is signalized both in the quantum and classical versions of the model. In the present contribution we show that not only the quantum ground state but also higher energy states, up to the energy of the corresponding classical separatrix orbit, "sense" the transition. We also show two types of one-to-one correspondences in this system: On the one hand, between the changes in the degree of entanglement for these low-lying quantum states and the changes in the density of energy levels; on the other hand, between the variation in the expected number of excitons for a given quantum state and the behavior of the corresponding classical orbit.
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Affiliation(s)
- Tathiana Moreira
- Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil.
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14
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Ribeiro P, Vidal J, Mosseri R. Thermodynamical limit of the Lipkin-Meshkov-Glick model. PHYSICAL REVIEW LETTERS 2007; 99:050402. [PMID: 17930734 DOI: 10.1103/physrevlett.99.050402] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2007] [Indexed: 05/25/2023]
Abstract
A method based on the analysis of the Majorana polynomial roots is introduced to compute the spectrum of the Lipkin-Meshkov-Glick model in the thermodynamical limit. A rich structure made of four qualitatively different regions is revealed in the parameter space, whereas the ground state study distinguishes between only two phases.
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Affiliation(s)
- Pedro Ribeiro
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France
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15
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16
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Cejnar P, Macek M, Heinze S, Jolie J, Dobeš J. Monodromy and excited-state quantum phase transitions in integrable systems: collective vibrations of nuclei. ACTA ACUST UNITED AC 2006. [DOI: 10.1088/0305-4470/39/31/l01] [Citation(s) in RCA: 101] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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17
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Leyvraz F, Heiss WD. Large-N scaling behavior of the Lipkin-Meshkov-Glick model. PHYSICAL REVIEW LETTERS 2005; 95:050402. [PMID: 16090853 DOI: 10.1103/physrevlett.95.050402] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2005] [Indexed: 05/03/2023]
Abstract
We introduce a novel semiclassical approach to the Lipkin model. In this way the well-known phase transition arising at the critical value of the coupling is intuitively understood. New results--showing for strong couplings the existence of a threshold energy which separates deformed from undeformed states as well as the divergence of the density of states at the threshold energy--are explained straightforwardly and in quantitative terms by the appearance of a double well structure in a classical system corresponding to the Lipkin model. Previously unnoticed features of the eigenstates near the threshold energy are also predicted and found to hold.
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Affiliation(s)
- F Leyvraz
- Centro de Ciencias Físicas, Universidad Nacional Autónoma de Mexico, Cuernavaca, 62551 Morelos, Mexico
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