First order dynamical phase transitions

Abstract

Recently, dynamical phase transitions have been identified based on the non-analytic behavior of the Loschmidt echo in the thermodynamic limit [Heyl et al., Phys.~Rev.~Lett.~{\bf 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 to use nonequilibrium dynamical mean-field theory to study the Loschmidt echo and dynamical phase transitions in high-dimensional, non-integrable models. We find dynamical phase transitions of first order in the Falicov-Kimball model and in the Hubbard model.

Published version, supplemental material included as appendix, 4 figures

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• Dynamical Quantum Phase Transitions in Systems with Continuous Symmetry Breaking
• Dynamical quantum phase transitions in the quantum Potts chain
• Time evolution during and after finite-time quantum quenches in the transverse-field Ising chain
• Exact out-of-time-ordered correlation functions for an interacting lattice fermion model
• Pulse and quench induced dynamical phase transition in a chiral multiferroic spin chain
• Nonequilibrium Dynamical Cluster Approximation study of the Falicov-Kimball Model
• Two rate periodic protocol with dynamics driven through many cycles