Finite-temperature mutual information in a simple phase transition

Author(s): J. Wilms, F. Verstraete, J. Vidal, S. Dusuel

Journal: Journal of Statistical Mechanics

Volume: 2012

Page(s): 01023

Year: 2012

DOI Number: 10.1088/1742-5468/2012/01/P01023

Link: Link to publication

Abstract:

We study the finite-temperature behavior of the Lipkin–Meshkov–Glick model with a focus on correlation properties as measured by the mutual information. The latter, which quantifies the amount of both classical and quantum correlations, is computed exactly in the two limiting cases of vanishing magnetic field and vanishing temperature. For all other situations, numerical results provide evidence of a finite mutual information at all temperatures except at criticality. There, it diverges as the logarithm of the system size, with a prefactor that can take only two values, depending on whether the critical temperature vanishes or not. Our work provides a simple example in which the mutual information appears as a powerful tool to detect finite-temperature phase transitions, contrary to entanglement measures such as the concurrence.

Note: http://arxiv.org/abs/1111.5225

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