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arXiv:1007.2182 · Physical Review B

Finite-size scaling of mutual information in Monte Carlo simulations: Application to the spin- 12 XXZ model

Roger G. Melko, Ann B. Kallin, Matthew B. Hastings

Published Sep 17, 2010• 91 citations
arXivHTMLPDF

Abstract

We develop a quantum Monte Carlo procedure to compute the Renyi mutual information of an interacting quantum many-body system at nonzero temperature. Performing simulations on a spin-$\frac{1}{2}$ $XXZ$ model, we observe that for a subregion of fixed size embedded in a system of size $L$, the mutual information converges at large $L$ to a limiting function which displays nonmonotonic temperature behavior corresponding to the onset of correlations. For a region of size $L/2$ embedded in a system of size $L$, the mutual information divided by $L$ converges to a limiting function of temperature, with apparently nontrivial corrections near critical points.

DOI
10.1103/physrevb.82.100409

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