Impact of quantum phase transitions on excited-level dynamics

Cejnar, Pavel; Stránský, Pavel

doi:10.1103/physreve.78.031130

Cited by 79 publications

(107 citation statements)

References 28 publications

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“…However, the maxima and minima still generate jumps in the DOQS at ε m,M . In undriven models these jumps would indicate a first order ESQPT [3]. In our driven model, however, they are just a consequence of the periodicity of the quasienergies.…”

Section: Fig 2 (Color Online)mentioning

confidence: 93%

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Quantum Criticality and Dynamical Instability in the Kicked-Top Model

et al. 2014

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We investigate precursors of critical behavior in the quasienergy spectrum due to the dynamical instability in the kicked top. Using a semiclassical approach, we analytically obtain a logarithmic divergence in the density of states, which is analogous to a continuous excited state quantum phase transition in undriven systems. We propose a protocol to observe the cusp behavior of the magnetization close to the critical quasienergy.PACS numbers: 05.30. Rt, 64.70.Tg, 05.45.Mt, 05.70.Fh The emerging field of excited state quantum phase transitions (ESQPTs) describes the nonanalytical behavior of excited states upon changes of parameters in the Hamiltonian [1][2][3]. This is in direct correspondence to quantum phase transitions (QPTs) [4], but takes place at critical energies above the ground state energy [5]. They entail dramatic dynamic consequences, e.g., environments with ESQPTs lead to enhanced decoherence, which could be a major drawback for building a quantum computer [6]. They appear in models of nuclear physics, such as the interacting Boson model [7,8] and the Lipkin-Meshkov-Glick model (LMG) [9]. In molecular physics, singularities of the density of states (DOS) arise in the vibron model [10], which are closely related to the monodromy in molecular bending degrees of freedom [11]. ESQPTs have been predicted to occur in prominent models of quantum optics such as the Dicke and Jaynes-Cummings models [12,13], too.Despite the striking observation of the QPT in the Dicke and the LMG model [14,15], ESQPTs have so far not been found experimentally for systems different to molecular ones, as the energies at which they occur are difficult to reach with standard techniques. Recently, however, the observation of low-energy singularities of the DOS in twisted graphene layers [16], and monodromy in diverse molecules [11], has opened an increasing interest in the experimental investigation of spectral singularities.Quantum critical behavior is usually defined with respect to system energies [4]. Under the effect of a nonadiabatic external control the energy is not conserved and it is not possible to uniquely define a ground state and the corresponding excited states. In this paper we make use of Floquet theory to introduce the concept of critical quasienergy states (CQS), which are a direct generalization of ESQPTs to driven quantum systems. Our model of choice is a paradigmatic model in the quantum chaos community: the kicked top. Quantum kicked systems play a prominent role in the investigation of quantum signatures of chaos and have intriguing relations to condensed matter systems [17]. Examples of these relations are the metal-supermetal [18] and metaltopological-insulator [19] QPTs in the kicked rotator, which can be thought of as a limiting case of the kicked top. Such a limit is established when the top is restricted to evolve along a small equatorial band, which is topologically equivalent to a cylinder [17].We are motivated by a recent experimental realization of the kicked top with driven ultra-cold Cesiuma...

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Section: Fig 2 (Color Online)mentioning

confidence: 93%

“…Rt, 64.70.Tg, 05.45.Mt, 05.70.Fh The emerging field of excited state quantum phase transitions (ESQPTs) describes the nonanalytical behavior of excited states upon changes of parameters in the Hamiltonian [1][2][3]. This is in direct correspondence to quantum phase transitions (QPTs) [4], but takes place at critical energies above the ground state energy [5].…”

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confidence: 99%

Quantum Criticality and Dynamical Instability in the Kicked-Top Model

et al. 2014

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“…Its quantum version [34] has been used to illustrate the effects associated with criticality as a prior step to deal with more involved physical situations [3,[34][35][36]. In addition to the cusp model, we present results for four different realizations of bosonic systems.…”

Section: Introductionmentioning

confidence: 99%

“…2 + vx is the cusp potential, with control parameters u and v and a classicality constant K = √ M , combining and the mass parameter M (see [35]). The smaller the value of K, the closer is the system to the classical limit.…”

Section: Selected Modelsmentioning

confidence: 99%

Identifying the order of a quantum phase transition by means of Wehrl entropy in phase space

et al. 2015

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“…More recently, considerable attention has been given to the so-called excited-state quantum phase transition (ESQPT) [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Unlike GSQPT, an ESQPT can occur not only with variation of the control parameters of a model Hamiltonian, but also with the increasing of the excitation energy.…”

Section: Introductionmentioning

confidence: 99%

Excited-state quantum phase transitions in the interacting boson model: Spectral characteristics of0+states and effective order parameter

2016

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The spectral characteristics of the L π = 0 + excited-states in the interacting boson model are systematically investigated. It is found that various types of excited-state quantum phase transitions may widely occur in the model as functions of the excitation energy, which indicates that the phase diagram of the interacting boson model can be dynamically extended along the direction of the excitation energy. It has also been justified that the d-boson occupation probability ρ(E) is qualified to be taken as the effective order parameter to identify these excited-state quantum phase transitions. In addition, the underlying relation between the excite-state quantum phase transition and the chaotic dynamics is also stated.

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Impact of quantum phase transitions on excited-level dynamics

Cited by 79 publications

References 28 publications

Quantum Criticality and Dynamical Instability in the Kicked-Top Model

Quantum Criticality and Dynamical Instability in the Kicked-Top Model

Identifying the order of a quantum phase transition by means of Wehrl entropy in phase space

Excited-state quantum phase transitions in the interacting boson model: Spectral characteristics of0+states and effective order parameter

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