Broken translation invariance in quasifree fermionic correlations out of equilibrium

TL;DR

This paper investigates how local magnetization breaking translation invariance affects correlations in a nonequilibrium steady state of the isotropic XY chain, revealing mathematical and physical impacts on decay behavior and scattering effects.

Contribution

It constructs a nonequilibrium steady state with broken translation invariance and analyzes the resulting correlation decay and scattering effects using C* algebraic methods.

Findings

Breaking translation invariance regularizes the Toeplitz operator symbol.

It introduces an additional trace class Hankel operator in the correlation determinant.

Decay rates reflect a left mover--right mover structure influenced by scattering.

Abstract

Using the C* algebraic scattering approach to study quasifree fermionic systems out of equilibrium in quantum statistical mechanics, we construct the nonequilibrium steady state in the isotropic XY chain whose translation invariance has been broken by a local magnetization and analyze the asymptotic behavior of the expectation value for a class of spatial correlation observables in this state. The effect of the breaking of translation invariance is twofold. Mathematically, the finite rank perturbation not only regularizes the scalar symbol of the invertible Toeplitz operator generating the leading order exponential decay but also gives rise to an additional trace class Hankel operator in the correlation determinant. Physically, in its decay rate, the nonequilibrium steady state exhibits a left mover--right mover structure affected by the scattering at the impurity.