Chaos in a deformed Dicke model

Corps, Ángel L.; Molina, Rafael A.; Relaño, Armando

doi:10.1088/1751-8121/ac4b16

Cited by 15 publications

(11 citation statements)

References 87 publications

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“…Remarkably, both the quantum and the classical versions of our impurity model exhibit a rich phenomenology, with regimes of chaos and integrability simultaneously present at different energies [43]. Notably, similar observations were made in various other models [42,46,64,65]. The classicalto-quantum correspondence of such models with mixed phase space is still an open question that could be investigated through the lens of an energy-resolved extension of BGS conjecture.…”

Section: Conclusion and Discussionsupporting

confidence: 53%

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Transition to chaos in extended systems and their quantum impurity models

Prasad¹,

Yadalam²,

Kulkarni³

et al. 2022

Preprint

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Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices. We consider an extended version of the Tavis-Cummings model on a finite chain. By studying level-spacing statistics, adjacent gap ratios, and spectral form factors, we observe the transition from integrability to chaos as the hopping between the Tavis-Cummings sites is increased above a finite value. The results are obtained by means of exact numerical diagonalization which becomes notoriously hard for extended lattice geometries. In an attempt to circumvent these difficulties, we identify a minimal single-site quantum impurity model which successfully captures the spectral properties of the lattice model. This approach is intended to be adaptable to other lattice models with large local Hilbert spaces.

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Section: Conclusion and Discussionsupporting

confidence: 53%

“…It corresponds to a single-site TC model with an additional drive term controlled by the parameter µ which breaks the U (1) symmetry as well as the integrability of the TC model. This type of models have been used in the literature to study the stability of the superradiant phase-transition and the onset of quantum chaos [41,42].…”

mentioning

confidence: 99%

Transition to chaos in extended systems and their quantum impurity models

Prasad¹,

Yadalam²,

Kulkarni³

et al. 2022

Preprint

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show abstract

“…An important feature is that Ĉ is not commuting with Π. For > the semiclassical phase space becomes connected, and Ĉ is no longer a conserved charge [36,58,59]. In the rest of this Letter, we derive a theory, and test it numerically, showing how the behavior of Ĉ triggers both kinds of DPTs.…”

mentioning

confidence: 99%

Theory of dynamical phase transitions in quantum systems with symmetry-breaking eigenstates

Corps¹,

Relaño²

2022

Preprint

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We present a theory for the two kinds of dynamical quantum phase transitions, sometimes termed DPT-I and DPT-II, in collective many-body systems. Both are triggered by excited-state quantum phase transitions. For quenches below the critical energy, the existence of an additional conserved charge, identifying the corresponding phase, allows for a non-zero value of the dynamical order parameter characterizing DPTs-I, and precludes the mechanism giving rise to non-analyticities in the return probability, trademark of DPTs-II. We propose a statistical ensemble describing the long-time averages of order parameters in DPTs-I, and provide a theoretical proof for the absence of true DPT-II critical times in the thermodynamic limit in the phase with this additional conserved charge. Our results are numerically illustrated in the fully-connected transverse-field Ising model, which exhibits both kinds of dynamical phase transitions.

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“…2(ac)]. It has been recently proposed [43,76,77] the classical constant of motion sign [ ( )] can be translated to the quantum domain by establishing a connection between quantum and classical dynamical functions. In this case, since ( , ) are bounded to the circumference of radius 2, 4 − 2 − 2 ≥ 0, and therefore Eq.…”

Section: A Semiclassical Analysismentioning

confidence: 99%

Dynamical and excited-state quantum phase transitions in collective systems

Corps,

Relaño

2022

Preprint

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We study dynamical phase transitions (DPTs) in quantum many-body systems with infinite-range interaction, and present a theory connecting the two kinds of known DPTs (sometimes referred to as DPTs-I and DPTs-II) with the concept of excited-state quantum phase transition (ESQPT), traditionally found in collective models. We show that DPTs-I appear as a manifestation of symmetry restoration after a quench from the broken-symmetry phase, the limits between these two phases being demarcated precisely by an ESQPT. We describe the order parameters of DPTs-I with a generalization of the standard microcanonical ensemble incorporating the information of an additional conserved charge identifying the corresponding phase. We also show that DPTs-I are linked to a mechanism of information erasure brought about by the ESQPT, and quantify this information loss with the statistical ensemble that we propose. Finally, we show analytically that DPTs-II are forbidden in these systems for quenches leading a broken-symmetry initial state to the same broken-symmetry phase, on one side of the ESQPT, and we provide a formulation of DPTs-II depending on the side of the ESQPT where the quench ends. We analyze the connections between various indicators of DPTs-II. Our results are numerically illustrated in the infinite-range transverse-field Ising model and are applicable to a large class of collective quantum systems satisfying a set of conditions.

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Chaos in a deformed Dicke model

Cited by 15 publications

References 87 publications

Transition to chaos in extended systems and their quantum impurity models

Transition to chaos in extended systems and their quantum impurity models

Theory of dynamical phase transitions in quantum systems with symmetry-breaking eigenstates

Dynamical and excited-state quantum phase transitions in collective systems

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