Excited-state quantum phase transitions in the two-spin elliptic Gaudin model

Relaño, Armando; Esebbag, C.; Dukelsky, J.

doi:10.1103/physreve.94.052110

Cited by 19 publications

(18 citation statements)

References 41 publications

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“…This is particularly complex for systems with several control parameters and a complex phase diagram. ESQPTs have been studied in different quantum many-body systems: the single [62] and coupled [69] Lipkin-Meshkov-Glick models, the Gaudin model [70], the Tavis-Cummings and Dicke models [63,71], the interacting boson model [50], the kicked-top model [72], periodic lattice models [73,74], or spinor Bose-Einstein condensates [75,76]. It has been paid special heed to the influence of ESQPTs on the dynamics of quantum systems [77][78][79][80][81][82][83][84][85][86][87] and to a possible link between ESQPTs and thermodynamic transitions [88,89].…”

Section: Introductionmentioning

confidence: 99%

Quantum fidelity susceptibility in excited state quantum phase transitions: application to the bending spectra of nonrigid molecules

2022

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We characterize excited state quantum phase transitions in the two dimensional limit of the vibron model with the quantum fidelity susceptibility, comparing the obtained results with the information provided by the participation ratio. As an application, we locate the eigenstate closest to the barrier to linearity and determine the linear or bent character of the different overtones for particular bending modes of six molecular species. We perform a fit and use the optimized eigenvalues and eigenstates in three cases and make use of recently published results for the other three cases.

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Section: Introductionmentioning

confidence: 99%

Quantum fidelity susceptibility in excited state quantum phase transitions: application to the bending spectra of nonrigid molecules

2022

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“…To shed some light on this important issue, and to get an idea of the expected finite-size effects, we rely on the semiclassical approximation. As shown in [44,70], we can use the standard Einstein-Brioullin-Keller (EBK) action quantization rules [71] to determine the positions of the energy levels of Eq. (2) in the thermodynamic limit.…”

Section: B Level Dynamicsmentioning

confidence: 99%

“…However, this is not necessarily true. It is also possible to find systems with ESQPTs without the corresponding QPT [44,45].…”

Section: Introductionmentioning

confidence: 99%

Energy cat states induced by a parity-breaking excited-state quantum phase transition

Corps,

Relaño

2022

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We show that excited-state quantum phase transitions (ESQPTs) in a system in which the parity symemtry has been broken can be used to engineer an energy-cat state -a Schrödinger cat state involving a quantum superposition of both different positions and energies. By means of a generalization of the Rabi model, we show that adding a parity-breaking term annihilates the ground-state quantum phase transition between normal and superradiant phases, and induces the formation of three excited-state phases, all of them identified by means of an observable with two eigenvalues. In one of these phases, level crossings are observed in the thermodynamic limit. We profit from them to separate a wavefunction in two parts: one, with lower energy, trapped within one region of the spectrum, and a second one, with higher energy, trapped within another. Finally, we show that a generalized microcanonical ensemble, including two different average energies, is required to properly describe equilibrium states in this situation. Our results illustrate yet another physical consequence of ESQPTs.

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“…(17) are not determined and may differ from those in Eq. (16). Degenerate stationary points (flatter than quadratic) may cause even sharper singularities, which however are not generally classified [7].…”

Section: Esqpts Due To Non-degenerate Stationary Pointsmentioning

confidence: 99%

Excited-state quantum phase transitions in systems with two degrees of freedom. III. Interacting boson systems

et al. 2019

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The series of articles [Ann. Phys. 345, 73 (2014) and 356, 57 (2015)] devoted to excited-state quantum phase transitions (ESQPTs) in systems with f = 2 degrees of freedom is continued by studying the interacting boson model of nuclear collective dynamics as an example of a truly manybody system. The intrinsic Hamiltonian formalism with angular momentum fixed to L = 0 is used to produce a generic first-order ground-state quantum phase transition with an adjustable energy barrier between the competing equilibrium configurations. The associated ESQPTs are shown to result from various classical stationary points of the model Hamiltonian, whose analysis is more complex than in previous cases because of (i) a non-trivial decomposition to kinetic and potential energy terms and (ii) the boundedness of the associated classical phase space. Finite-size effects resulting from a partial separability of both degrees of freedom are analyzed. The features studied here are inherent in a great majority of interacting boson systems.

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Excited-state quantum phase transitions in the two-spin elliptic Gaudin model

Cited by 19 publications

References 41 publications

Quantum fidelity susceptibility in excited state quantum phase transitions: application to the bending spectra of nonrigid molecules

Quantum fidelity susceptibility in excited state quantum phase transitions: application to the bending spectra of nonrigid molecules

Energy cat states induced by a parity-breaking excited-state quantum phase transition

Excited-state quantum phase transitions in systems with two degrees of freedom. III. Interacting boson systems

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