  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.

Statistical Mechanics;Quantum Gases;Quantum Physics