Using tensor network methods, we simulate the real-time evolution of the lattice Thirring model quenched out of equilibrium in both the critical and massive phases, and study the appearance of dynamical quantum phase transitions, as non-analyticities in the Loschmidt rate. Whereas the presence of a dynamical quantum phase transition in the model does not correspond to quenches across the critical line of the equilibrium phase diagram at zero temperature, we identify a threshold in the energy density of the initial state, necessary for a dynamical quantum phase transition to be present. Moreover, in the case of the gapped quench Hamiltonian, we unveil a connection of this threshold to a transition between different regions in the finite temperature phase diagram.
Bañuls et al. (Wed,) studied this question.