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arXiv · 1101.0430

Finite Temperature Critical Behavior of Mutual Information

Rajiv R. P. Singh·Matthew B. Hastings·Ann B. Kallin·Roger G. Melko
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Abstract

We study mutual information for Renyi entropy of arbitrary index n, in interacting quantum systems at finite-temperature critical points, using high-temperature expansion, quantum Monte Carlo simulations and scaling theory. We find that for n>1, the critical behavior is manifest at two temperatures T_c and n*T_c. For the XXZ model with Ising anisotropy, the coefficient of the area-law has a t*ln(t) singularity, whereas the subleading correction from corners has a logarithmic divergence, with a coefficient related to the exact results of Cardy and Peschel. For T<n*T_c there is a constant term associated with broken symmetries that jumps at both T_c and n*T_c, which can be understood in terms of a scaling function analogous to the boundary entropy of Affleck and Ludwig.

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Rajiv R. P. Singh, Matthew B. Hastings, Ann B. Kallin, Roger G. Melko. 2011-03-04. Finite Temperature Critical Behavior of Mutual Information. https://doi.org/10.1103/physrevlett.106.135701

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