Ruelle-Lanford functions for quantum spin systems

TL;DR

This paper establishes a large deviation principle for macroscopic observables in quantum and classical Gibbs states using Ruelle-Lanford functions, providing a unified approach that extends classical results to quantum systems.

Contribution

It introduces a novel proof method for large deviations in quantum Gibbs states using Ruelle-Lanford functions, avoiding traditional quantum-specific techniques.

Findings

Unified framework for quantum and classical large deviations

Extension of classical large deviation results to quantum lattice systems

Recovery and expansion of existing quantum large deviation results

Abstract

We prove a large deviation principle for the expectation of macroscopic observables in quantum (and classical) Gibbs states. Our proof is based on Ruelle-Lanford functions and direct subadditivity arguments, as in the classical case, instead of relying on G\"artner-Ellis theorem, and cluster expansion or transfer operators as done in the quantum case. In this approach we recover, expand, and unify quantum (and classical) large deviation results for lattice Gibbs states. In the companion paper \cite{OR} we discuss the characterization of rate functions in terms of relative entropies.