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

2022/11/17 by Marcel Rodekamp, Rodekamp, Marcel, Christoph Gäntgen +1
Materials Science · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Machine Learning in Materials Science #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2211.09584

openalex publication_date 2022/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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