Exact dynamical correlations of nonlocal operators in quadratic open Fermion systems: a characteristic function approach

TL;DR

This paper introduces a characteristic function approach to analyze dynamical correlations of nonlocal operators in quadratic open fermion systems, revealing new insights into quantum phase transitions and nonlocal excitations.

Contribution

The paper develops a novel characteristic function method for open fermion systems and applies it to analyze nonlocal operator correlations and dynamical quantum phase transitions.

Findings

Asymmetric light cone induced by anyon statistics

Relaxation rate increases with anyon statistical parameter

Signatures of nonequilibrium quantum phase transition and dynamical quantum phase transitions

Abstract

The dynamical correlations of nonlocal operators in general quadratic open fermion systems is still a challenging problem. Here we tackle this problem by developing a new formulation of open fermion many-body systems, namely, the characteristic function approach. Illustrating the technique, we analyze a finite Kitaev chain with boundary dissipation and consider anyon-type nonlocal excitations. We give explicit formula for the Green's functions, demonstrating an asymmetric light cone induced by the anyon statistical parameter and an increasing relaxation rate with this parameter. We also analyze some other types of nonlocal operator correlations such as the full counting statistics of the charge number and the Loschmidt echo in a quench from the vacuum state. The former shows clear signature of a nonequilibrium quantum phase transition, while the later exhibits cusps at some critical times and hence demonstrates dynamical quantum phase transitions.