Journal of Physics A Mathematical and Theoretical

Distribution of quantum correlations and conditional entropy in Heisenberg spin chains

Aritra Kundu, V. Subrahmanyam

Published Oct 11, 2013• 6 citations

Abstract

The quantum discord, which quantifies the amount of quantum correlation present between parts of a system, is investigated for spin systems. The discord for a pair of spins in the many-spin ground state, computed by minimizing the conditional entropy of the two spins, is related to the diagonal and off-diagonal spin–spin correlation functions and the local magnetization. We show that for isotropic and translationally invariant states, the discord depends only on the diagonal spin correlation function. Thus, near a thermal/quantum critical point, the pairwise discord exhibits long-range behavior, analogously to the correlation function. The discord exhibits a kink singularity as a function of the anisotropy parameter for the ground state of the anisotropic Heisenberg model, for both nearest-neighbor spins as well as for well-separated spins. The preferred measurement basis for the minimum conditional entropy, which determines the discord, changes discontinuously across the critical point. We also investigate, from exact numerical diagonalization, the distribution of conditional entropies as the measurement basis is varied. For the isotropic model, the conditional entropy distribution is a δ-function, whereas it has a twin-peak structure for the anisotropic model. It is shown that the average value and the mean-square fluctuation of the conditional entropy also show a signature of the critical-point behavior.

DOI: 10.1088/1751-8113/46/43/435304

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