Scaling of quantum discord in spin models

TL;DR

This paper analyzes how quantum discord, a measure of quantum correlations, scales in various spin models, revealing area law behavior at finite temperature and decay patterns at zero temperature.

Contribution

It provides an analytical and systematic study of quantum discord scaling in spin models, including explicit calculations for several key chains.

Findings

Quantum discord obeys an area law at finite temperature.

Two-site quantum discord decays exponentially in gapped and gapless systems at zero temperature.

Quantum discord scaling resembles that of correlation functions in these models.

Abstract

We study the scaling of quantum discord (a measure of quantum correlation beyond entanglement) in spin models analytically and systematically. We find that at finite temperature the block scaling of quantum discord satisfies an area law for any two-local Hamiltonian. We show that generically and heuristically the two-site scaling of quantum discord is similar to that of correlation functions. In particular, at zero temperature it decays exponentially and polynomially in gapped and gapless (critical) systems, respectively; at finite temperature it decays exponentially in both gapped and gapless systems. We compute the two-site scaling of quantum discord in the XXZ chain, the XY chain (in a magnetic field), and the transverse field Ising chain at zero temperature.