Chiral condensate in the Schwinger model with Matrix Product Operators

TL;DR

This paper demonstrates the effectiveness of Matrix Product Operators in analyzing the Schwinger model at finite temperature, providing insights into chiral symmetry breaking and showcasing potential for tackling the sign problem in lattice gauge theories.

Contribution

The study extends tensor network methods to finite temperature in the Schwinger model, highlighting their potential for non-zero chemical potential and real-time simulations.

Findings

Method accurately captures chiral symmetry breaking.

Works well across a broad temperature range.

Shows promise for addressing the sign problem in QCD.

Abstract

Tensor network (TN) methods, in particular the Matrix Product States (MPS) ansatz, have proven to be a useful tool in analyzing the properties of lattice gauge theories. They allow for a very good precision, much better than standard Monte Carlo (MC) techniques for the models that have been studied so far, due to the possibility of reaching much smaller lattice spacings. The real reason for the interest in the TN approach, however, is its ability, shown so far in several condensed matter models, to deal with theories which exhibit the notorious sign problem in MC simulations. This makes it prospective for dealing with the non-zero chemical potential in QCD and other lattice gauge theories, as well as with real-time simulations. In this paper, using matrix product operators, we extend our analysis of the Schwinger model at zero temperature to show the feasibility of this approach also at finite temperature. This is an important step on the way to deal with the sign problem of QCD. We analyze in detail the chiral symmetry breaking in the massless and massive cases and show that the method works very well and gives good control over a broad range of temperatures, essentially from zero to infinite temperature.