Entanglement echo and dynamical entanglement transitions

Pöyhönen, Kim; Ojanen, Teemu

doi:10.1103/physrevresearch.3.l042027

Cited by 11 publications

(3 citation statements)

References 46 publications

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“…Finally, we note that in the isolated Kitaev chain, the soft-mode period t s,+ = t s,− coincides with the period of zeros of the Loschmidt echo, which are known as dynamical quantum phase transitions [66,67], and can be understood as a consequence of quenching between topologically distinct phases [68]. The question whether a suitabel generalization of the Loschmidt echo to open systems [69][70][71] can capture the existence of two distinct time scales t s,+ t s,− warrants further investigation.…”

mentioning

confidence: 91%

Relaxation to a parity-time symmetric generalized Gibbs ensemble after a quantum quench in a driven-dissipative Kitaev chain

Starchl¹,

Sieberer²

2022

Preprint

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The construction of the generalized Gibbs ensemble, to which isolated integrable quantum many-body systems relax after a quantum quench, is based upon the principle of maximum entropy. In contrast, there are no universal and model-independent laws that govern the relaxation dynamics and stationary states of open quantum systems, which are subjected to Markovian drive and dissipation. Yet, as we show, relaxation of driven-dissipative systems after a quantum quench can, in fact, be determined by a maximum entropy ensemble, if the Liouvillian that generates the dynamics of the system has parity-time symmetry. Focusing on the specific example of a driven-dissipative Kitaev chain, we show that, similarly to isolated integrable systems, the approach to a parity-time symmetric generalized Gibbs ensemble becomes manifest in the relaxation of local observables and the dynamics of entanglement. In contrast, the directional pumping of fermion parity, which is induced by nontrivial non-Hermitian topology of the Kitaev chain, represents a phenomenon that is unique to relaxation dynamics in driven-dissipative systems. Upon increasing the strength of dissipation, parity-time symmetry is broken at a finite critical value, which thus constitutes a sharp dynamical transition that delimits the applicability of the principle of maximum entropy. While we focus here on the specific example of the Kitaev chain, our results generalize readily to all parity-time symmetric and integrable driven-dissipative systems that are described by or can be mapped to noninteracting fermions.

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mentioning

confidence: 91%

Relaxation to a parity-time symmetric generalized Gibbs ensemble after a quantum quench in a driven-dissipative Kitaev chain

Starchl¹,

Sieberer²

2022

Preprint

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“…The concept of DQPT emanates from the analogy between the equilibrium partition function of a system, and Loschmidt amplitude, which measures the overlap between an initial state and its time-evolved one . As the equilibrium phase transition is signaled by non-analyticities in the thermal free energy, the DQPT is revealed through the nonanalytical behavior of dynamical free energy, where the real-time plays the role of the control parameter [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. DQPT displays a phase transition between dynamically emerging quantum phases, that takes place during the nonequilibrium coherent quantum time evolution under sudden/ramped quench or timeperiodic modulation of Hamiltonian [16,[85][86][87][88][89][90][91].…”

Section: Introductionmentioning

confidence: 99%

Scaling and universality at ramped quench dynamical quantum phase transitions

Zamani,

Naji,

Jafari

et al. 2024

J. Phys.: Condens. Matter

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The nonequilibrium dynamics of a periodically driven extended XY model, in the presence oflinear time dependent magnetic filed, is investigated using the notion of dynamical quantum phasetransitions (DQPTs). Along the similar lines to the equilibrium phase transition, the main purposeof this work is to search the fundamental concepts such as scaling and universality at the rampedquench DQPTs. We have shown that the critical points of the model, where the gap closing occurs,can be moved by tuning the driven frequency and consequently the presence/absence of DQPTscan be flexibly controlled by adjusting the driven frequency. We have uncovered that, for a rampacross the single quantum critical point, the critical mode at which DQPTs occur is classified intothree regions: the Kibble-Zurek (KZ) region, where the critical mode scales linearly with the squareroot of the sweep velocity, pre-saturated (PS) region, and the saturated (S) region where the criticalmode makes a plateau versus the sweep velocity. While for a ramp that crosses two critical points,the critical modes disclose just KZ and PS regions. On the basis of numerical simulations, we findthat the dynamical free energy scales linerly with time, as approaches to DQPT time, with theexponent ν = 1 ± 0.01 for all sweep velocities and driven frequencies.

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“…In addition, the nonequilibrium dynamics of the Anderson model after a quench of the disorder strength has also been explored 24 . The concept of dynamical phase transitions may also be characterized by entanglement echo 28 – 30 (the overlap of the initial and its time-evolved entanglement Hamiltonian ground states) of the subsystems embedded in a larger quantum systems. Moreover, the DQPTs can be probed by measuring the nonequilibrium order parameter in the Lipkin–Meshkov–Glick model with a quenched transverse field 31 .…”

Section: Introductionmentioning

confidence: 99%

Anomalous correlation-induced dynamical phase transitions

Khan

Wang

Jan

et al. 2023

Sci Rep

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The nonanalyticity of the Loschmidt echo at critical times in quantum quenched systems is termed as the dynamical quantum phase transition, extending the notion of quantum criticality to a nonequilibrium scenario. In this paper, we establish a new paradigm of dynamical phase transitions driven by a sudden change in the internal spatial correlations of the disorder potential in a low-dimensional disordered system. The quench dynamics between prequenched pure and postquenched random system Hamiltonian reveals an anomalous dynamical quantum phase transition triggered by an infinite disorder correlation in the modulation potential. The physical origin of the anomalous phenomenon is associated with the overlap between the two distinctly different extended states. Furthermore, we explore the quench dynamics between the prequenched random and postquenched pure system Hamiltonian. Interestingly, the quenched system undergoes dynamical quantum phase transitions for the prequench white-noise potential in the thermodynamic limit. In addition, the quench dynamics also shows a clear signature of the delocalization phase transition in the correlated Anderson model.

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Entanglement echo and dynamical entanglement transitions

Cited by 11 publications

References 46 publications

Relaxation to a parity-time symmetric generalized Gibbs ensemble after a quantum quench in a driven-dissipative Kitaev chain

Relaxation to a parity-time symmetric generalized Gibbs ensemble after a quantum quench in a driven-dissipative Kitaev chain

Scaling and universality at ramped quench dynamical quantum phase transitions

Anomalous correlation-induced dynamical phase transitions

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