Scaling behaviors of correlation measures in quantum spin systems

We aim to study the scaling behaviors of important correlation measures including entanglement entropy and the newly proposed measure of purely quantum correlations, quantum discord (QD), which quantifies all nonclassical correlations including entanglement as a subset, in general quantum spin systems. In this work we emphasize on the latter measure (QD) and present the explicit derivation of the relations between QD and spin-correlation functions in Z2-symmetric quantum spin lattice models, which are powerful tools for studying pairwise QD behaviors in these models, and analyze Heisenberg XXZ chain as an example, in the critical regime of which the QD is shown to decay polynomially at zero temperature, but with different critical exponent as of correlation functions. We also prove an area law for QD scaling in general noncritical quantum spin systems with local interactions, in contrast to the expected extensive behavior.