Anharmonicity-induced excited-state quantum phase transition in the symmetric phase of the two-dimensional limit of the vibron model

Khalouf-Rivera, Jamil; Pérez‐Bernal, F.; Carvajal, M.

doi:10.1103/physreva.105.032215

Cited by 13 publications

(16 citation statements)

References 94 publications

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“…Figure 1(b) is the correlation energy diagram for a negative α value. As expected from the results obtained for the twodimensional limit of the vibron model [29,30], there is a new separatrix that crosses the one associated with the groundstate QPT and the degeneracy pattern is more complex. In order to better understand the second separatrix we study the classical limit of the model, making use of the spin coherent states formalism [74].…”

Section: Modelsupporting

confidence: 65%

“…Inspired by the work in Refs. [29,30], we include in the Hamiltonian (2) an anharmonic term, using a second-order operator on Ŝz ,…”

Section: Modelmentioning

confidence: 99%

“…[29] it was shown that the inclusion of anharmonicity in the Hamiltonian results in a second ESQPT in the broken-symmetry phase, which is where the typical spectroscopic signatures of nonrigid molecules are found. More recently, in the pursuit of the description of the transition state in isomerization reactions [18], it has been found that the second ESQPT can also be present in the symmetric phase for sufficiently large values of the anharmonicity and it is not associated with the ground-state QPT but it stems from changes in the phase-space boundary of the 2DVM's finite-dimensional Hilbert space [30].…”

Section: Introductionmentioning

confidence: 99%

“…Our aim is to extend the results obtained for the 2DVM [29,30] to the Lipkin-Meshkov-Glick (LMG) model. This model was introduced as a toy model for interacting fermions in nuclear physics, to help assess the performance of different approximations used in the study of nuclear structure [32][33][34].…”

Section: Introductionmentioning

confidence: 99%

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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: Modelsupporting

confidence: 65%

“…Inspired by the work in Refs. [29,30], we include in the Hamiltonian (2) an anharmonic term, using a second-order operator on Ŝz ,…”

Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…Inspired by the works in Refs. [34,35], we have included in the Eq. ( 1) Hamiltonian a second-order Casimir operator of u(2), S 2 z ,…”

Section: The Modelmentioning

confidence: 99%

Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model II: Dynamical Aspects

Khalouf-Rivera¹,

Gamito²,

Pérez‐Bernal³

et al. 2022

Preprint

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It is worth noting that phase transitions are well defined for macroscopic systems, however, the same ideas can be applied when studying mesoscopic systems where one can observe phase transition precursors even for moderate system sizes [30]. Hence, when dealing with mesoscopic systems, the study of their mean field or large-size limit to connect with thermodynamic phase transitions is a valuable reference. Exactly-solvable models, such as the LMG model, are simple enough to be solved for a large number of particles, allowing for a clear connection with the aforementioned large-size limit. This work is part of a more complete study on the anharmonic LMG (aLMG) model. The additional anharmonic term induces, in addition to the already known ESQPT [27,31], an anharmonicity-induced ESQPT that needs to be well understood. In a previous publication [32], the static aspects of both the ground state QPT and the two ESQPT's in the aLMG model were characterized. A mean field analysis in the large-N limit was performed and different observables were used to characterize the different quantum phase transitions involved: the energy gap between adjacent levels, the ground state QPT order parameter, the participation ratio, the quantum fidelity susceptibility, and the level density. In this work, we concentrate on the influence of the two ESQPTs on the dynamics of the aLMG model. With this aim, a quantum quench protocol that consists of an abrupt change in one of the control parameters in the aLMG Hamiltonian is defined. Then, the evolution of the system after the quench is studied using

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Spectral kissing and its dynamical consequences in the squeeze-driven Kerr oscillator

et al. 2023

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Transmon qubits are the predominant element in circuit-based quantum information processing, such as existing quantum computers, due to their controllability and ease of engineering implementation. But more than qubits, transmons are multilevel nonlinear oscillators that can be used to investigate fundamental physics questions. Here, they are explored as simulators of excited state quantum phase transitions (ESQPTs), which are generalizations of quantum phase transitions to excited states. We show that the spectral kissing (coalescence of pairs of energy levels) experimentally observed in the effective Hamiltonian of a driven SNAIL-transmon is an ESQPT precursor. We explore the dynamical consequences of the ESQPT, which include the exponential growth of out-of-time-ordered correlators, followed by periodic revivals, and the slow evolution of the survival probability due to localization. These signatures of ESQPT are within reach for current superconducting circuits platforms and are of interest to experiments with cold atoms and ion traps.

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Anharmonicity-induced excited-state quantum phase transition in the symmetric phase of the two-dimensional limit of the vibron model

Cited by 13 publications

References 94 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

Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model II: Dynamical Aspects

Spectral kissing and its dynamical consequences in the squeeze-driven Kerr oscillator

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