Classical Correlation and Quantum Discord in Critical Systems

TL;DR

This paper analyzes how classical and quantum correlations, measured by quantum discord, behave in critical quantum systems, revealing signatures of quantum phase transitions through analytical and numerical methods.

Contribution

It provides analytical expressions for correlations in symmetric systems and applies them to multiple models, highlighting their behavior near quantum critical points.

Findings

Quantum discord signals quantum phase transitions.

Correlations exhibit distinct behavior in critical regimes.

Analytical formulas derived for systems with $Z_2$ symmetry.

Abstract

We discuss the behavior of quantum and classical pairwise correlations in critical systems, with the quantumness of the correlations measured by the quantum discord. We analytically derive these correlations for general real density matrices displaying $Z_2$ symmetry. As an illustration, we analyze both the XXZ and the transverse field Ising models. Finite-size as well as infinite chains are investigated and the quantum criticality is discussed. Moreover, we identify the spin functions that govern the correlations. As a further example, we also consider correlations in the Hartree-Fock ground state of the Lipkin-Meshkov-Glick model. It is then shown that both classical correlation and quantum discord exhibit signatures of the quantum phase transitions.