Mitigating the Hubbard Sign Problem. A Novel Application of Machine Learning

TL;DR

This paper introduces a neural network approach to mitigate the Hubbard sign problem by transforming integration domains, enabling simulations of strongly correlated electron systems with severe sign issues.

Contribution

A novel complex-valued neural network architecture based on affine coupling layers for efficient domain transformation in sign problem mitigation.

Findings

Successfully applied to the Hubbard model at finite chemical potential.

Demonstrates improved efficiency in handling complex action sign problems.

Enables simulations previously hindered by the sign problem.

Abstract

Many fascinating systems suffer from a severe (complex action) sign problem preventing us from calculating them with Markov Chain Monte Carlo simulations. One promising method to alleviate the sign problem is the transformation of the integration domain towards Lefschetz Thimbles. Unfortunately, this suffers from poor scaling originating in numerically integrating of flow equations and evaluation of an induced Jacobian. In this proceedings we present a new preliminary Neural Network architecture based on complex-valued affine coupling layers. This network performs such a transformation efficiently, ultimately allowing simulation of systems with a severe sign problem. We test this method within the Hubbard Model at finite chemical potential, modelling strongly correlated electrons on a spatial lattice of ions.