Trajectory phase transitions, Lee-Yang zeros, and high-order cumulants in full counting statistics

TL;DR

This paper links dynamical phase transitions in stochastic many-body systems to the behavior of high-order cumulants of observables, enabling detection of phase transitions through accessible measurements.

Contribution

It establishes a general relation between Lee-Yang zeros, high-order cumulants, and dynamical phase transitions in full counting statistics.

Findings

High-order cumulants reveal dynamical phase transitions.

Short-time cumulant behavior indicates transition locations.

Connection between large-deviation theory and experimental observables.

Abstract

We investigate Lee-Yang zeros of generating functions of dynamical observables and establish a general relation between phase transitions in ensembles of trajectories of stochastic many-body systems and the time evolution of high-order cumulants of such observables. This connects dynamical free-energies for full counting statistics in the long-time limit, which can be obtained via large-deviation methods and whose singularities indicate dynamical phase transitions, to observables that are directly accessible in simulation and experiment. As an illustration we consider facilitated spin models of glasses and show that from the short-time behavior of high-order cumulants it is possible to infer the existence and location of dynamical or "space-time" transitions in these systems.