Towards overcoming the Monte Carlo sign problem with tensor networks

TL;DR

This paper demonstrates that tensor network methods can effectively address the sign problem in lattice gauge theories at finite density, enabling accurate calculations where traditional Monte Carlo methods fail.

Contribution

The authors extend tensor network techniques to two-flavor models with non-zero chemical potential, successfully overcoming the sign problem in lattice gauge theories.

Findings

Tensor networks reproduce known analytical results at finite density.

They successfully compute the mass spectrum and thermal properties.

The approach overcomes the sign problem in non-zero chemical potential scenarios.

Abstract

The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density.