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

Fernández, Pedro Pérez; Relaño, Armando

doi:10.1103/physreve.96.012121

Cited by 44 publications

(33 citation statements)

References 47 publications

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“…In recent years, another type of quantum transition has been observed in collective models, where the excited states change their characteristics at a critical energy density corresponding to the singularities of density of states. Such transition is termed as excited state quantum phase transition (ESQPT) [6][7][8][9][10][11][12], however its connection with thermodynamic behavior of physical quantities deserves further attention [6,11]. The non-equilibrium dynamics of a closed quantum system reveals various interesting phenomena related to ergodicity of the system, where the excited states also play a crucial role [4,13].…”

Section: Introductionmentioning

confidence: 99%

Chaos and quantum scars in a coupled top model

Mondal

Sinha

2020

Phys. Rev. E

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We consider an interacting collective spin model known as coupled top (CT), exhibiting a rich variety of phenomena related to quantum transitions and ergodicity, which we explore and find their connection with underlying dynamics. The ferromagnetic interaction between the spins leads to the quantum phase transition (QPT) as well as a dynamical transition at a critical coupling strength, and both the transitions are accompanied by excited state quantum phase transitions at critical energy densities. Above QPT, the onset of chaos in the CT model occurs in an intermediate coupling strength, which is analyzed both classically and quantum mechanically. However, a detailed analysis reveals the presence of non-ergodic multifractal eigenstates in the chaotic regime. We quantify the degree of ergodicity of the eigenstates from the relative entanglement entropy and multifractal dimensions, revealing its variation with energy density across the energy band. We probe such energy dependent ergodic behavior of states from non-equilibrium dynamics, which is also supplemented by phase space mixing in classical dynamics. Moreover, we identify another source of deviation from ergodicity due to the formation of 'quantum scars' arising from the unstable steady states and periodic orbits. Unlike the ergodic states, the scarred eigenstates violate Berry's conjecture even in the chaotic regime, leading to the athermal non-ergodic behavior. Finally, we discuss the detection of non-ergodic behavior and dynamical signature of quantum scars by using 'out-of-time-order correlator', which has relevance in the recent experiments.

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Section: Introductionmentioning

confidence: 99%

Chaos and quantum scars in a coupled top model

Mondal

Sinha

2020

Phys. Rev. E

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“…The excited-state quantum phase transition influence on the dynamics of quantum systems has recently attracted significant attention and several remarkable dynamical effects of excited-state quantum phase transitions have been revealed [22,24,26,[36][37][38][39][40][41][42][43]. In particular, the impact of excited-state quantum phase transitions on the adiabatic dynamics of a quantum system has been recently analyzed [44], as well as the relationship between thermal phase transitions and excitedstate quantum phase transitions [45].…”

Section: Introductionmentioning

confidence: 99%

Excited-state quantum phase transition and the quantum-speed-limit time

Wang

Pérez‐Bernal

2019

Phys. Rev. A

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We investigate the influence of an excited-state quantum phase transition on the quantum speed limit time of an open quantum system. The system consists of a central qubit coupled to a spin environment modeled by a Lipkin-Meshkov-Glick Hamiltonian. We show that when the coupling between qubit and environment is such that the latter is located at the critical energy of the excitedstate quantum phase transition, the qubit evolution shows a remarkable slowdown, marked by an abrupt peak in the quantum speed limit time. Interestingly, this slowdown at the excited-state quantum phase transition critical point is induced by the singular behavior of the qubit decoherence rate, being independent of the Markovian nature of the environment.

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“…As paradigmatic examples, we highlight recent experimental results involving systems with just one [4][5][6][7][8][9][10], and two semiclassical degrees of freedom [11]. Non-usual thermodynamics have been already reported on some of them [12][13][14]. In this Letter we show that the process of equilibration and thermalisation is also anomalous in the Dicke [15] and the Lipkin-Meshkov-Glick (LMG) [16] models, realized in some of the previously quoted experiments [5,6,11].…”

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confidence: 98%

Anomalous Thermalization in Quantum Collective Models

Relaño

2018

Phys. Rev. Lett.

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We show that apparently thermalised states still store relevant amounts of information about their past, information that can be tracked by experiments involving non-equilibrium processes. We provide a condition for the microcanonical quantum Crook's theorem, and we test it by means of numerical experiments. In the Lipkin-Meshkov-Glick model, two different procedures leading to the same equilibrium states give rise to different statistics of work in non-equilibrium processes. In the Dicke model, two different trajectories for the same non-equilibrium protocol produce different statistics of work. Microcanonical averages provide the correct results for the expectation values of physical observables in all the cases; the microcanonical quantum Crook's theorem fails, in some of them. We conclude that testing quantum fluctuation theorems is mandatory to verify if a system is properly thermalised.

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

Cited by 44 publications

References 47 publications

Chaos and quantum scars in a coupled top model

Chaos and quantum scars in a coupled top model

Excited-state quantum phase transition and the quantum-speed-limit time

Anomalous Thermalization in Quantum Collective Models

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