Edge exponents in work statistics out of equilibrium and dynamical phase transitions from scattering theory in one dimensional gapped systems

TL;DR

This paper explores how edge exponents in work statistics relate to dynamical phase transitions and excitations in non-equilibrium, gapped one-dimensional systems, revealing their insensitivity to interactions and their connection to symmetry and bound states.

Contribution

It demonstrates that edge exponents are unaffected by interactions and identifies their possible values, linking them to symmetry breaking, bound states, and dynamical phase transitions.

Findings

Edge exponents can only be +1/2, -1/2, or -3/2.

Presence of one-particle channels induces dynamical phase transitions.

Edge exponents are insensitive to interactions.

Abstract

I discuss the relationship between edge exponents in the statistics of work done, dynamical phase transitions, and the role of different kinds of excitations appearing when a non-equilibrium protocol is performed on a closed, gapped, one-dimensional system. I show that the edge exponent in the probability density function of the work is insensitive to the presence of interactions and can take only one of three values: +1/2, -1/2 and -3/2. It also turns out that there is an interesting interplay between spontaneous symmetry breaking or the presence of bound states and the exponents. For instantaneous global protocols, I find that the presence of the one-particle channel creates dynamical phase transitions in the time evolution.