Dynamical quantum phase transitions: A brief survey

Abstract

Nonequilibrium states of closed quantum many-body systems defy a thermodynamic description. As a consequence, constraints such as the principle of equal a priori probabilities in the microcanonical ensemble can be relaxed, which can lead to quantum states with novel properties of genuine nonequilibrium nature. In turn, for the theoretical description it is in general not sufficient to understand nonequilibrium dynamics on the basis of the properties of the involved Hamiltonians. Instead it becomes important to characterize time-evolution operators which adds time as an additional scale to the problem. In these Perspectives we summarize recent progress in the field of dynamical quantum phase transitions, which are phase transitions in time with temporal nonanalyticities in matrix elements of the time-evolution operator. These transitions are not driven by an external control parameter, but rather occur due to sharp internal changes generated solely by unitary real-time dynamics. We discuss the obtained insights on general properties of dynamical quantum phase transitions, their physical interpretation, potential future research directions, as well as recent experimental observations.

Operator content of entanglement spectra in the transverse field Ising chain after global quenches

“…The possibility of defining scaling and universality when crossing several dynamical quantum phase transitions is still debated [66]. Our results seem to indicate that this is the case when the entanglement spectrum is considered.…”

“…By quenching across the QPT of the Ising model we encounter a dynamical quantum phase transition [64]. A dynamical quantum phase transition occurs at times when the return probability to the original state after the quench vanishes (see [66] for a recent review). Usual quantum phase transitions induce a universal behavior of correlation functions.…”

“…[63] for a recent experiment and references). Dynamical quantum phase transitions, appearing as singularities in the return probabilities to the initial state quenched across a quantum critical point, could also provide a scaling region explainable through outof-equilibrium universality [64][65][66].…”

Wehrl entropy production rate across a dynamical quantum phase transition

“…On the experimental side, we can mention the observation of DPTs in the Ising model in an ion trap [7], in the topological phase in the Haldane model using optical lattices [8], and in a simulation of the Ising model in a quantum computer [9]. We refer the reader to the recent reviews [10][11][12] for further details about this field.…”

“…[10] for more details). Despite considerable progress in our understanding of DPTs, several open questions still remain, for instance, regarding their universality and if they can be captured from macroscopic properties [10][11][12]. In this article we focus on two deeply related questions.…”