Large Deviation Functions for Open Quantum Systems with a Strong Symmetry

TL;DR

This paper develops a method to derive large deviation functions in open quantum systems with strong symmetries, overcoming nonanalyticities in the global scaled cumulant generating function by local analysis.

Contribution

It introduces a block-wise application of the G"artner-Ellis theorem and demonstrates it with analytical and spin models, revealing phenomena like avoided level crossings.

Findings

Global SCGF nonanalyticity due to strong symmetry

Local rate functions obtained via G"artner-Ellis theorem

Avoided level crossing observed in spin model with dephasing

Abstract

In open quantum systems with strong symmetries, the global scaled cumulant generating function (SCGF) is generally nonanalytic, so the G\"artner-Ellis theorem cannot directly yield the genuine large-deviation rate function. To address this issue, we propose that the theorem remains valid within blocks of the systems' operator space: we first obtain local rate functions for each block via the theorem and then recover the global one by minimization. This approach is justified by the dissipative freezing phenomenon in such systems. We demonstrate the scheme in an analytical model and a three-spin model with XX interaction. In the latter, we find that the vanishing of a nonanalytic point in the global SCGF under dephasing appears as an avoided ``level'' crossing, and we quantify this behavior using a degenerate perturbation theory.