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Equivalence of Statistical Mechanical Ensembles for Non-Critical Quantum Systems

Fri, 2016-06-03 15:11 - Oliver Marty
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Date: 
2015-02-11
Author(s): 

Fernando G.S.L. Brandao, Marcus Cramer

Reference: 

arXiv:1502.03263

URL: 

http://arxiv.org/abs/1502.03263

We consider the problem of whether the canonical and microcanonical ensembles are locally equivalent for short-ranged quantum Hamiltonians ofN 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(N1/(d+1)) spins. The proof rests on a variant of the Berry--Esseen theorem for quantum lattice systems and ideas from quantum information theory.