Dynamical Quantum Phase Transitions Following Double Quenches: Persistence of the Initial State vs Dynamical Phases

TL;DR

This paper investigates how double quenches in quantum systems influence dynamical quantum phase transitions, revealing conditions under which these transitions occur depending on the phases of initial, intermediate, and final Hamiltonians.

Contribution

It provides a comprehensive analysis of the response of quantum states to double quenches, highlighting the role of phase differences and timing in the emergence of dynamical quantum phase transitions.

Findings

Dynamical quantum phase transitions occur when initial and final Hamiltonians are in different phases.

If initial and final Hamiltonians are in the same phase, the intermediate phase must differ for transitions to occur.

The timing of the second quench relative to critical times affects the presence of transitions.

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.