Theory of dynamical phase transitions in collective quantum systems

Ángel L. Corps, Armando Relaño

Published 2022-05-06Version 1

We present a theory for the two kinds of dynamical quantum phase transitions, sometimes termed DPT-I and DPT-II, in collective many-body systems. Both are triggered by excited-state quantum phase transitions. For quenches below the critical energy, the existence of an additional conserved charge, identifying the corresponding phase, allows for a non-zero value of the dynamical order parameter characterizing DPTs-I, and precludes the mechanism giving rise to non-analyticities in the return probability, trademark of DPTs-II. We propose a statistical ensemble describing the long-time averages of order parameters in DPTs-I, and provide a theoretical proof for the absence of true DPT-II critical times in the thermodynamic limit in the phase with this additional conserved charge. Our results are numerically illustrated in the fully-connected transverse-field Ising model, which exhibits both kinds of dynamical phase transitions.