Entanglement asymmetry in gauge theories: chiral anomaly in the finite temperature massless Schwinger model

TL;DR

This paper investigates entanglement asymmetry in the massless Schwinger model, revealing its sensitivity to chiral symmetry-breaking and phase transitions at finite temperature, thus establishing it as a useful probe in gauge theories.

Contribution

First study of entanglement asymmetry in gauge theories, demonstrating its behavior and potential as a phase transition probe in the Schwinger model at finite temperature.

Findings

Entanglement asymmetry grows logarithmically with system size at zero temperature.

At finite temperature, asymmetry decreases logarithmically, more slowly than the chiral condensate.

Asymmetry is more sensitive to chiral symmetry-breaking than local order parameters.

Abstract

The entanglement asymmetry has emerged in recent years as a practical quantity to study phases of matter. We present the first study of entanglement asymmetry in gauge theories by considering the chiral anomaly of the analytically solvable massless Schwinger model at both zero and finite temperatures. At zero temperature, we find the asymmetry exhibits logarithmic growth with system size. At finite temperature, we show that it is parametrically more sensitive to chiral symmetry-breaking than the corresponding local order parameter: while the chiral condensate decays exponentially, the asymmetry decreases only logarithmically. This establishes the entanglement asymmetry as a promising tool to probe (finite-temperature) phase transitions in gauge theories.