Vortex loop dynamics and dynamical quantum phase transitions in 3D fermion matter

Arkadiusz Kosior, Markus Heyl

Published 2023-07-06Version 1

In this study, we investigate the behavior of vortex singularities in the phase of the Green's function of a general non-interacting fermionic lattice model in three dimensions after an instantaneous quench. We find that the full set of vortices form one-dimensional dynamical objects, which we call vortex loops. The number of such vortex loops can be interpreted as a quantized order parameter that distinguishes between different non-equilibrium phases. We show that changes in this order parameter are related to dynamical quantum phase transitions (DQPTs). Our results are applicable to general lattice models in three dimensions. For concreteness, we present them in the context of a simple two-band Weyl semimetal. We also show that the vortex loops survive in weakly interacting systems. Finally, we observe that vortex loops can form complex dynamical patterns in momentum space due to the existence of band touching Weyl nodes. Our findings provide valuable insights for developing definitions of dynamical order parameters in non-equilibrium systems.