Mitigating the Hubbard sign problem with complex-valued neural networks

Rodekamp, Marcel, Berkowitz, Evan, Gaentgen, Christoph, Krieg, Stefan, Luu, Thomas and Ostmeyer, Johann ORCID: 0000-0001-7641-8030 (2022) Mitigating the Hubbard sign problem with complex-valued neural networks. PHYSICAL REVIEW B, 106 (12). 125139-.

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Official URL: http://dx.doi.org/10.1103/physrevb.106.125139

Abstract

Monte Carlo simulations away from half filling suffer from a sign problem that can be reduced by deforming the contour of integration. Such a transformation, which induces a Jacobian determinant in the Boltzmann weight, can be implemented using neural networks. This additional determinant cost for a generic neural network scales cubically with the volume, preventing large-scale simulations. We implement an architecture, based on complex-valued affine coupling layers, which reduces this to linear scaling. We demonstrate the efficacy of this method by successfully applying it to systems of different size, the largest of which is intractable by other Monte Carlo methods due to its severe sign problem.

Item Type:	Article
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	07 Mar 2023 16:21
Last Modified:	15 Mar 2024 18:36
DOI:	10.1103/PhysRevB.106.125139
Open Access URL:	https://arxiv.org/pdf/2203.00390.pdf
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3168831