Mitigating the Hubbard Sign Problem with Complex-Valued Neural Networks

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 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.

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Cited by in corpus (12)

• Exploring QCD matter in extreme conditions with Machine Learning
• Flow-based density of states for complex actions
• Improving efficiency of the path optimization method for a gauge theory
• Fermionic Sign Problem Minimization by Constant Path Integral Contour Shifts
• On the Infinite Variance Problem in Fermion Models
• Real Time Simulations of Quantum Spin Chains: Density-of-States and Reweighting approaches
• Application of the path optimization method to a discrete spin system
• Single Particle Spectrum of Doped ${\mathrm{C}}_{20}{\mathrm{H}}_{12}$-Perylene
• Reducing the Sign Problem with simple Contour Deformation
• Is it worth the effort to find Lefschetz thimbles? Integration contours with numerically optimal signal-to-noise ratios in simple fermionic toy models
• Stochastic and Tensor Network simulations of the Hubbard Model
• Path optimization method for the sign problem caused by fermion determinant