First-Order Dynamical Phase Transitions

Recently, dynamical phase transitions have been identified based on the nonanalytic behavior of the Loschmidt echo in the thermodynamic limit Heyl et al., Phys. Rev. Lett. 110, 135704 (2013). By introducing conditional probability amplitudes, we show how dynamical phase transitions can be further classified, both mathematically, and potentially in experiment. This leads to the definition of first-order dynamical phase transitions. Furthermore, we develop a generalized Keldysh formalism which allows us to use nonequilibrium dynamical mean-field theory to study the Loschmidt echo and dynamical phase transitions in high-dimensional, nonintegrable models. We find dynamical phase transitions of first order in the Falicov-Kimball model and in the Hubbard model.