  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.
