Schwinger model at finite temperature and density with beta VQE

TL;DR

This paper applies a variational quantum algorithm to study the phase diagram of the massless Schwinger model at finite temperature and density, demonstrating the method's effectiveness and exploring its phase structure.

Contribution

The study adapts $eta$-VQE for finite temperature and density, providing a new quantum computational approach to analyze gauge theories' phase diagrams.

Findings

The variational algorithm works for $T>0$ and $>0$ in the Schwinger model.

No significant volume dependence of the free energy in the studied parameter range.

Qualitative phase diagram of the massless Schwinger model obtained.

Abstract

We investigate a quantum gauge theory at finite temperature and density using a variational algorithm for near-term quantum devices. We adapt $\beta$-VQE to evaluate thermal and quantum expectation values and study the phase diagram for massless Schwinger model along with the temperature and density. By compering the exact variational free energy, we find the variational algorithm work for $T>0$ and $\mu>0$ for the Schwinger model. No significant volume dependence of the variational free energy is observed in $\mu/g \in[0, 1.4]$. We calculate the chiral condensate and take the continuum extrapolation. As a result, we obtain qualitative picture of the phase diagram for massless Schwinger model.