Dynamical quantum phase transitions following double quenches: persistence of the initial state vs dynamical phases

Abstract

Dynamical quantum phase transitions can occur following quenches in quantum systems when the rate function, a dynamical analogue of the free energy, becomes non-analytic at critical times. Here we exhaustively investigate in an exemplary model how the dynamically evolving state responds to a second quench. We demonstrate that for quenches where the initial and final Hamiltonian belong to different phases always result in dynamical quantum phase transitions, irrespective of the intermediate quench and dynamics or the time of the second quench. However, if the initial and final Hamiltonian belong to the same equilibrium phase then the intermediate Hamiltonian must belong to a different phase. In this case, the second quench time in relation to the critical times of the first quench becomes crucial to the existence of dynamical quantum phase transitions.

Resilience of quantum spin fluctuations against Dzyaloshinskii–Moriya interaction

“…In Ref. 45 although the authors studied the effect of the DMI on the quantum speed limit and orthogonality catastrophe under sudden quantum quenches, their results spontaneously affirmed the robustness of the initial quantum spin fluctuations against the DMI in a nonequilibrium quantum system which can be also interpreted as the persistence of the initial state versus dynamical phases 46 , 47 . This resiliency also can be observed in the behavior of the spin-spin correlation functions in the equilibrium 48 .…”

Scaling and universality at ramped quench dynamical quantum phase transitions

“…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].…”