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Finite Temperature Critical Behavior of Mutual Information · Around

2011

Finite Temperature Critical Behavior of Mutual Information

Singh, Rajiv R. P., Hastings, Matthew B., Kallin, Ann B. et al.

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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.

Built on

H. Au-Yang and M. E. Fisher, Phys. Rev. B 11
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J. L. Cardy and I. Peschel, Nuclear Physics B 300
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M. P. Gelfand, R. R. P. Singh, and D. A. Huse, J. Stat. Phys. 59
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I. Affleck and A. W. W. Ludwig, Phys. Rev. Lett. 67
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A. W. Sandvik and J. Kurkijärvi, Phys. Rev. B 43
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Then

A. B. Kallin, I. González, M. B. Hastings, and R. G. Melko, Phys. Rev. Lett. 103
2009
Later among the works it cites.
T. Nishioka, S. Ryu, and T. Takayanagi, J. Phys. A 42
2009
Later among the works it cites.
M. B. Hastings, I. González, A. B. Kallin, and R. G. Melko, Phys. Rev. Lett. 104
2010
Later among the works it cites.
R. G. Melko, A. B. Kallin, and M. B. Hastings, Phys. Rev. B 82
2010
Later among the works it cites.
S. Isakov, M. B. Hastings, and R. G. Melko, arXiv:1102.1721 (2011)
Original
2011
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