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Finite Temperature Critical Behavior of Mutual Information

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.