Heat capacity for systems with excited-state quantum phase transitions

Cejnar, Pavel; Stránský, Pavel

doi:10.1016/j.physleta.2017.01.022

Cited by 9 publications

(10 citation statements)

References 26 publications

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“…A possible explanation, compatible with Ref. [24], is that, in this case, the number of effective degrees of freedom becomes infinite, since we have an infinite number of j sectors (each one with f = 2 degrees of freedom) in the thermodynamical limit.…”

Section: E Numerical Results: Esqpt Versus Thermal Phase Transitionmentioning

confidence: 57%

“…As it is pointed out in Ref. [24] this is due to the finite number of (semiclassical) degrees of freedom that the system has in the thermodynamic limit, N → ∞. …”

Section: Resultsmentioning

confidence: 97%

“…Indeed, it is shown in Ref. [24] that, for collective systems, the thermodynamical limit N → ∞ does not coincide with the true thermodynamic limit unless the number of degree of freedom, f , also tends to infinity. So, ESQPTs and thermal phase transitions appear for different asymptotic regimes of N and f .…”

Section: Introductionmentioning

confidence: 99%

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From thermal to excited-state quantum phase transition: The Dicke model

Fernández

Relaño

2017

Phys. Rev. E

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We study the thermodynamics of the full version of the Dicke model, including all the possible values of the total angular momentum j , with both microcanonical and canonical ensembles. We focus on both the excited-state quantum phase transition, appearing in the microcanonical description of the maximum angular momentum sector, j = N/2, and the thermal phase transition, which occurs when all the sectors are taken into account. We show that two different features characterize the full version of the Dicke model. If the system is in contact with a thermal bath and is described by means of the canonical ensemble, the parity symmetry becomes spontaneously broken at the critical temperature. In the microcanonical ensemble, and despite that all the logarithmic singularities which characterize the excited-state quantum phase transition are ruled out when all the j sectors are considered, there still exists a critical energy (or temperature) dividing the spectrum into two regions: one in which the parity symmetry can be broken, and another in which this symmetry is always well defined.

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Section: E Numerical Results: Esqpt Versus Thermal Phase Transitionmentioning

confidence: 57%

“…As it is pointed out in Ref. [24] this is due to the finite number of (semiclassical) degrees of freedom that the system has in the thermodynamic limit, N → ∞. …”

Section: Resultsmentioning

confidence: 97%

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From thermal to excited-state quantum phase transition: The Dicke model

Fernández

Relaño

2017

Phys. Rev. E

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“…It has been found that ESQPT plays an important role in several contexts including quantum decoherence process [16][17][18], quantum chaos [19][20][21][22], and quantum thermodynamics [23,24]. Many efforts have been devoted to understand the intriguing properties, both statical [25][26][27][28][29][30][31] and dynamical [32][33][34][35][36][37][38][39], of this new kind phase transition.…”

Section: Introductionmentioning

confidence: 99%

Characterizing the excited-state quantum phase transition via the dynamical and statistical properties of the diagonal entropy

Wang,

Pérez-Bernal

2020

Preprint

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Using the diagonal entropy we analyze the dynamical signatures of the excited-state quantum phase transitions (ESQPT) in the Lipkin-Meshkov-Glick (LMG) model. We first show that the time evolution of the diagonal entropy behaves as an efficient indicator of the presence of ESQPT. We further consider the diagonal entropy as a random variable over a certain time interval and focus on the statistical properties of the diagonal entropy. We find that the probability distribution of the diagonal entropy provides a clear distinction between different phases of ESQPT. In particular, we observe that at the critical point the probability distribution of the diagonal entropy has a universal form, which can be well described by the so-called beta distribution. We finally demonstrate the central moments of the diagonal entropy can reliably detect the critical point of ESQPT.

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“…This singularity is present in the spectral level density and in related quantities, e.g., in the flow rate, which is an average slope of the quantum spectrum when λ is varied. The existence of an esqpt also influences the canonical and microcanonical thermodynamics [9,10,11,12], decoherence and relaxation processes [13,14,15], driven and dissipative dynamics [16,17], and entanglement properties [18].…”

Section: Introductionmentioning

confidence: 99%

Excited-state quantum phase transitions and their manifestations in an extended Dicke model

Stránský

Kloc

Cejnar

2017

AIP Conference Proceedings

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Abstract. An Excited-State Quantum Phase Transition (esqpt) is a singularity observed in quantum energy spectra in the infinitesize limit of the system. It originates in the existence of stationary points in the semiclassical Hamiltonian function. We review the classification of esqpts and present a case study in an extended Dicke model. Finally, we show some preliminary results on the dynamical effect induced by esqpts.

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Heat capacity for systems with excited-state quantum phase transitions

Cited by 9 publications

References 26 publications

From thermal to excited-state quantum phase transition: The Dicke model

From thermal to excited-state quantum phase transition: The Dicke model

Characterizing the excited-state quantum phase transition via the dynamical and statistical properties of the diagonal entropy

Excited-state quantum phase transitions and their manifestations in an extended Dicke model

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