Relation between quantum phase transitions and classical instability points in the pairing model

Reis, Maurício Sedrez dos; Cunha, Marcelo Terra; Oliveira, Adélcio C.; Nemes, M. C.

doi:10.1016/j.physleta.2005.06.064

Cited by 13 publications

(21 citation statements)

References 7 publications

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“…A chain of ESQPTs affecting energy levels E i with increasing excitation index i usually originates from the ground-state QPT affecting E 0 at λ c0 . So far, such effects have been studied mostly in integrable systems with one effective degree of freedom (one-dimensional configuration spaces) showing a singularity in their classical dynamics at a certain energy [19][20][21][22][23][24][25][26], but they seem to exist in a much richer variety of incarnations.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, the level density can form an infinite peak at E = E c (λ) (in contrast to thermodynamic systems whose level density is always an increasing function of energy). The peak in ρ(E,λ) is accompanied by vanishing slope and diverging curvature of individual energy levels crossing the critical boundary E c (λ) [16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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Quantum quench influenced by an excited-state phase transition

et al. 2011

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We analyze excited-state quantum phase transitions (ESQPTs) in three schematic (integrable and nonintegrable) models describing a single-mode bosonic field coupled to a collection of atoms. It is shown that the presence of the ESQPT in these models affects the quantum relaxation processes following an abrupt quench in the control parameter. Clear-cut evidence of the ESQPT effects is presented in integrable models, while in a nonintegrable model the evidence is blurred due to chaotic behavior of the system in the region around the critical energy.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum quench influenced by an excited-state phase transition

et al. 2011

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“…3, where maximal level densities appear as minimal differences for adjacent energy levels. It has been shown [26,28] that in these Curie-Weiss models a quantum phase transition is connected with the level approximation, occurring maximally at these inflection points. We will also see that in the thermodynamic limit the inflection point is associated with a separatrix orbit in the corresponding classical phase space.…”

Section: B An Effective Hamiltonianmentioning

confidence: 99%

“…The closed orbits correspond to classical energies less than h(j z = −1) or greater than h(j z = 1). The arising of the separatrix in phase space is associated to the level approximation in the quantum spectrum [26,28]. This can be seen in the three cases below:…”

Section: Classical Thermodynamic Limit Of the Hamiltonianmentioning

confidence: 99%

Quantum phase transition in an effective three-mode model of interacting bosons

et al. 2017

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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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“…On the other hand, the excited-state QPTs have been so far described only in the simplest situations. The existing studies refer mostly to systems with an effective number of degrees of freedom f = 1, like the Lipkin model [21], the two-and three-dimensional vibron models for a subset of states with angular momentum l = 0 [22], the interacting boson model along its O(6)-U(5) transition for a subset of states with angular momentum and seniority l = v = 0 [18], a so-called cusp Hamiltonian [20], or schematic pairing models [19,23,24]. New results concern the JaynesCummings model of quantum optics and a related model based on the SU(1,1) dynamical algebra [25].…”

Section: Example: Ibm In the Su(3) Limitmentioning

confidence: 99%

Quantum phase transitions in finite algebraic systems

Cejnar

2011

J. Phys.: Conf. Ser.

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Abstract. We discuss features of quantum phase transitions affecting collective dynamics of many-body systems. Due to a finite number of collective degrees of freedom, the infinitesize limit of the corresponding models coincides with the classical limit and quantum critical phenomena for both the ground and excited states are determined by the structure of the classical phase space. An example of an excited-state phase transition for the interacting boson model in its SU(3) limit is presented.

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Relation between quantum phase transitions and classical instability points in the pairing model

Cited by 13 publications

References 7 publications

Quantum quench influenced by an excited-state phase transition

Quantum quench influenced by an excited-state phase transition

Quantum phase transition in an effective three-mode model of interacting bosons

Quantum phase transitions in finite algebraic systems

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