First order dynamical phase transitions

TL;DR

This paper introduces a classification of dynamical phase transitions, including first-order types, using conditional probabilities and a generalized Keldysh formalism to analyze models like Hubbard and Falicov-Kimball.

Contribution

It develops a new framework for classifying dynamical phase transitions and extends nonequilibrium dynamical mean-field theory to study these phenomena in complex models.

Findings

First-order dynamical phase transitions identified in Hubbard and Falicov-Kimball models.

Generalized Keldysh formalism enables analysis of Loschmidt echo in high-dimensional systems.

Classification scheme links mathematical properties with experimental observability.

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.