Dynamical Quantum Phase Transitions in the Lattice Thirring and XXZ Models

We investigate dynamical quantum phase transitions (DQPTs) in the lattice Thirring model and the 1D XXZ model by simulating quench dynamics using the infinite-size Time-Dependent Variational Principle (TDVP) tensor network algorithm. The Thirring model is discretized on an infinite 1D lattice, and we focus on the nonanalytical points of the return rate function, which define DQPTs. Our results show that for both models, DQPTs occur only when the energy surpasses a critical threshold, starting from various initial states with different energies. Additionally, we simulate the effective inverse temperature β and map DQPTs on the β-time plane. We also perform complex-time evolution to identify Fisher zeros through the nonanalytical points in the return rate function. The connection between DQPTs on the β-time plane and Fisher zeros remains an open question for further investigation.