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Mitigating the Hubbard Sign Problem with Complex-Valued Neural Networks
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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 a new 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.
Forward citations
Cited by 2 Pith papers
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Exploring Group Convolutional Networks for Sign Problem Mitigation via Contour Deformation
Group convolutional networks with built-in lattice symmetries outperform fully connected networks for learned contour deformations in small Hubbard-model sign-problem simulations, but transfer learning across paramete...
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Path optimization method for the sign problem caused by fermion determinant
Path optimization with machine learning reproduces analytic results in the 1D lattice Thirring model, and dropping the Jacobian from the learning step still works.
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