Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model

Gutiérrez‐Ruiz, Daniel; González, Diego López; Chávez-Carlos, Jorge; Hirsch, Jorge G.; Vergara, J. David

doi:10.1103/physrevb.103.174104

Cited by 18 publications

(11 citation statements)

References 78 publications

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“…It can be mapped to a set of spins with a long-range all-to-all interaction, and from their initial purpose it was later used in many different contexts. In particular, it was extensively used for the study of QPTs [35][36][37][38][39][40][41][42][43][44][45] and ESQPTs [46][47][48][49][50][51][52][53][54][55]. The general LMG model presents first-, second-, and third-order ground-state QPTs [43], something that has attracted the interest of researchers.…”

Section: Introductionmentioning

confidence: 99%

Excited-state quantum phase transitions in the anharmonic Lipkin-Meshkov-Glick model: Static aspects

Gamito

Khalouf-Rivera²,

Arias³

et al. 2022

Phys. Rev. E

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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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Section: Introductionmentioning

confidence: 99%

Excited-state quantum phase transitions in the anharmonic Lipkin-Meshkov-Glick model: Static aspects

Gamito

Khalouf-Rivera²,

Arias³

et al. 2022

Phys. Rev. E

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“…Therefore, we infer that in the thermodynamic limit, the discontinuity of the scalar curvature (which is −4 in the symmetric phase and does not exist in the broken phase) is the cause of the singularity in the derivative at the QPT. In another work [24], we explore a modified LMG model that has an invertible metric in both phases and makes this point clearer, showing without doubt that the scalar curvature is discontinuous at the QPT in the thermodynamic limit, which causes the divergence in its derivative there.…”

Section: Numerical Analysis For Finite Jmentioning

confidence: 99%

“…Nevertheless, the dependence of the coherent states' coordinates on the Hamiltonian parameters might constitute a noninvertible mapping, which then results in a QMT whose components are zero in one or both phases of the system. Therefore, this semiclassical version of the QMT is useless to characterize the geometry of the parameter space [24]. On the other hand, the classical metric shows its relevance emerging as a tool that, through purely classical functions and a classical torus average, provides a result consistent with the quantum description in many cases.…”

Section: Introductionmentioning

confidence: 99%

Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models

Gonzalez,

Gutiérrez-Ruiz,

Vergara

2021

Preprint

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We study the classical analog of the quantum metric tensor and its scalar curvature for two well-known quantum physics models. First, we analyze the geometry of the parameter space for the Dicke model with the aid of the classical and quantum metrics and find that, in the thermodynamic limit, they have the same divergent behavior near the quantum phase transition, as opposed to their corresponding scalar curvatures which are not divergent there. On the contrary, under resonance conditions, both scalar curvatures exhibit a divergence at the critical point. Second, we present the classical and quantum metrics for the Lipkin-Meshkov-Glick model in the thermodynamic limit and find a perfect agreement between them. We also show that the scalar curvature is only defined on one of the system's phases and that it approaches a negative constant value. Finally, we carry out a numerical analysis for the system's finite sizes, which clearly shows the precursors of the quantum phase transition in the metric and its scalar curvature and allows their characterization as functions of the parameters and of the system's size.

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“…It can be mapped to a set of spins with a long range all-to-all interaction, and from their initial purpose it has been later used in many different contexts. In particular, it has been extensively used for the study of QPTs [33][34][35][36][37][38][39][40][41][42][43][44] and ESQPTs [45][46][47][48][49][50][51][52]. The general LMG model presents first-, second-and third-order ground state QPTs [42], something that has attracted the interest of researchers.…”

Section: Introductionmentioning

confidence: 99%

Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model I: Static Aspects

Gamito¹,

Khalouf-Rivera²,

Arias³

et al. 2022

Preprint

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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 new 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.

show abstract

Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model

Cited by 18 publications

References 78 publications

Excited-state quantum phase transitions in the anharmonic Lipkin-Meshkov-Glick model: Static aspects

Excited-state quantum phase transitions in the anharmonic Lipkin-Meshkov-Glick model: Static aspects

Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models

Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model I: Static Aspects

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