Equivalence of Statistical Mechanical Ensembles for Non-Critical Quantum Systems

Abstract

We consider the problem of whether the canonical and microcanonical ensembles are locally equivalent for short-ranged quantum Hamiltonians of $N$ spins arranged on a $d$-dimensional lattices. For any temperature for which the system has a finite correlation length, we prove that the canonical and microcanonical state are approximately equal on regions containing up to $O(N^{1/(d+1)})$ spins. The proof rests on a variant of the Berry--Esseen theorem for quantum lattice systems and ideas from quantum information theory.

References in corpus (4)

• The large deviation approach to statistical mechanics
• Normal approximation under local dependence
• Smooth Renyi Entropies and the Quantum Information Spectrum
• Complex-Time Singularity and Locality Estimates for Quantum Lattice Systems

Cited by in corpus (2)

• Thermalization of locally perturbed many-body quantum systems
• Theoretical study on thermalization in isolated quantum systems