Criticality, factorization and long-range correlations in the anisotropic XY-model

TL;DR

This paper investigates long-range quantum correlations in the anisotropic XY-model, revealing how quantum discord captures key features, exhibits simple scaling at finite temperatures, and relates to ground-state factorization, with small systems approximating the thermodynamic limit.

Contribution

It introduces a comprehensive analysis of quantum correlations, factorization, and finite-size effects in the anisotropic XY-model, highlighting new scaling behaviors and the relevance of small systems.

Findings

Quantum discord captures main features at zero temperature.

Correlations obey simple scaling at finite temperatures.

Small systems can approximate the thermodynamic limit.

Abstract

We study the long-range quantum correlations in the anisotropic XY-model. By first examining the thermodynamic limit we show that employing the quantum discord as a figure of merit allows one to capture the main features of the model at zero temperature. Further, by considering suitably large site separations we find that these correlations obey a simple scaling behavior for finite temperatures, allowing for efficient estimation of the critical point. We also address ground-state factorization of this model by explicitly considering finite size systems, showing its relation to the energy spectrum and explaining the persistence of the phenomenon at finite temperatures. Finally, we compute the fidelity between finite and infinite systems in order to show that remarkably small system sizes can closely approximate the thermodynamic limit.