Distribution of quantum discord in Heisenberg Antiferromagnets

TL;DR

This paper explores how quantum discord, a measure of quantum correlations, behaves in antiferromagnetic Heisenberg models, revealing critical point signatures and long-range correlations related to spin interactions.

Contribution

It establishes a relationship between quantum discord and spin correlation functions in Heisenberg antiferromagnets, highlighting critical behavior and measurement basis discontinuities.

Findings

Quantum discord relates to spin correlation functions.

Long-range discord near critical points.

Discontinuous change in measurement basis at criticality.

Abstract

The quantum discord, which quantifies the amount of quantum correlations present between parts of a system, is investigated for antiferromagnetic spin systems. The discord for a pair of spins in the many-spin ground state is related to the diagonal and off-diagonal spin-spin correlation functions and the local magnetization. For isotropic and translationally invariant states, the discord is shown to be a function of the diagonal correlation function only. Thus, near a thermal/quantum critical point, the discord for a pair of spins shows long-range behavior, analogously of the correlation function. The discord exhibits a kink singularity as a function of the anisotropy parameter for the the ground state of the 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. The conditional entropy distribution over all possible the measurement basis is investigated. For the isotropic model, the distribution is just a delta-function, whereas it has a twin-peak structure for 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.