Time-integrated observables as order parameters for dynamical phase transitions in closed quantum systems

TL;DR

This paper introduces the use of time-integrated observables as order parameters to identify and analyze dynamical phase transitions in closed quantum systems, exemplified by the quantum Ising chain.

Contribution

It demonstrates how the analytic properties of generating functions of time-integrated observables reveal dynamical phases and transitions, independent of initial conditions or external protocols.

Findings

Identification of a continuum of quantum dynamical transitions in the quantum Ising chain

Dynamical transitions are detectable via full-counting statistics and quantum jump analysis

Proposed experimental realization using digital quantum simulation with cold ions

Abstract

The dynamical behaviour of many-body systems is often richer than what can be anticipated from their static properties. Here we show that in closed quantum systems this becomes evident by considering time-integrated observables as order parameters. In particular, the analytic properties of their generating functions, as estimated by full-counting statistics, allow to identify dynamical phases, i.e. phases with specific fluctuation properties of time-integrated observables, and to locate the transitions between these phases. We discuss in detail the case of the quantum Ising chain in a transverse field. We show that this model displays a continuum of quantum dynamical transitions, of which the static transition is just an end point. These singularities are not a consequence of particular choices of initial conditions or other external non-equilibrium protocols such as quenches in coupling constants. They can be probed generically through quantum jump statistics of an associated open problem, and for the case of the quantum Ising chain we outline a possible experimental realisation of this scheme by digital quantum simulation with cold ions.