The multi-flavor Schwinger model with chemical potential - Overcoming the sign problem with Matrix Product States

TL;DR

This paper demonstrates the use of matrix product states to study the multi-flavor Schwinger model at non-zero chemical potential, overcoming the sign problem and analyzing spatially resolved chiral condensates.

Contribution

The study extends tensor network methods to analyze spatially resolved properties of the multi-flavor Schwinger model at finite density.

Findings

Recovered spatial oscillations of the chiral condensate

Oscillation frequency depends on chemical potential

Amplitude matches zero-density condensate value

Abstract

During recent years there has been an increasing interest in the application of matrix product states, and more generally tensor networks, to lattice gauge theories. This non-perturbative method is sign problem free and has already been successfully used to compute mass spectra, thermal states and phase diagrams, as well as real-time dynamics for Abelian and non-Abelian gauge models. In previous work we showed the suitability of the method to explore the zero-temperature phase structure of the multi-flavor Schwinger model at non-zero chemical potential, a regime where the conventional Monte Carlo approach suffers from the sign problem. Here we extend our numerical study by looking at the spatially resolved chiral condensate in the massless case. We recover spatial oscillations, similar to the theoretical predictions for the single-flavor case, with a chemical potential dependent frequency and an amplitude approximately given by the homogeneous zero density condensate value.