Out-of-equilibrium phase diagram of long-range superconductors

TL;DR

This paper maps the out-of-equilibrium phase diagram of long-range superconductors, revealing how dynamical criticality relates to equilibrium properties and connecting theoretical predictions with experimental observations.

Contribution

It provides the first comprehensive dynamical phase diagram for long-range superconductors with analytic and numerical evidence linking nonanalyticities to topological features.

Findings

Dynamical phase transitions are characterized by nonanalyticities in the return rate.

Zero crossings of the string order parameter indicate dynamical critical points.

Results explain experimental observations of dynamical vortices in topological systems.

Abstract

Within the ultimate goal of classifying universality in quantum many-body dynamics, understanding the relation between out-of-equilibrium and equilibrium criticality is a crucial objective. Models with power-law interactions exhibit rich well-understood critical behavior in equilibrium, but the out-of-equilibrium picture has remained incomplete, despite recent experimental progress. We construct the rich dynamical phase diagram of free-fermionic chains with power-law hopping and pairing, and provide analytic and numerical evidence showing a direct connection between nonanalyticities of the return rate and zero crossings of the string order parameter. Our results may explain the experimental observation of so-called \textit{accidental} dynamical vortices, which appear for quenches within the same topological phase of the Haldane model, as reported in [Fl\"aschner \textit{et al.}, Nature Physics \textbf{14}, 265 (2018)]. Our work is readily applicable to modern ultracold-atom experiments, not least because state-of-the-art quantum gas microscopes can now reliably measure the string order parameter, which, as we show, can serve as an indicator of dynamical criticality.