A remark on the subleading order in the asymptotics of the nonequilibrium emptiness formation probability

TL;DR

This paper investigates the asymptotic decay of the emptiness formation probability in a nonequilibrium steady state of the XY chain, revealing a nonvanishing subleading power law decay caused by singularities.

Contribution

It demonstrates that, unlike equilibrium cases, the subleading power law exponent in nonequilibrium states is strictly positive, due to singularities in the steady state density.

Findings

Exponential decay of the emptiness formation probability.

Presence of a nonvanishing subleading power law decay.

Singularities in the steady state density influence asymptotics.

Abstract

We study the asymptotic behavior of the emptiness formation probability for large spin strings in a translation invariant quasifree nonequilibrium steady state of the isotropic XY chain. Besides the overall exponential decay, we prove that, out of equilibrium, the exponent of the subleading power law contribution to the asymptotics is nonvanishing and strictly positive due to the singularities in the density of the steady state.