Machine learning to alleviate Hubbard-model sign problems

Wynen, Jan-Lukas; Berkowitz, Evan; Krieg, Stefan; Luu, Thomas; Ostmeyer, Johann

doi:10.1103/physrevb.103.125153

Title: Machine learning to alleviate Hubbard-model sign problems

Journal Article · Thu Mar 25 00:00:00 EDT 2021 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.103.125153· OSTI ID:1850040

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Forschungszentrum Jülich (Germany)
Univ. of Maryland, College Park, MD (United States); Forschungszentrum Jülich (Germany)
Forschungszentrum Jülich (Germany); Rheinische Friedrich-Wilhelms-Univ. Bonn (Germany)
Rheinische Friedrich-Wilhelms-Univ. Bonn (Germany)

Lattice Monte Carlo calculations of interacting systems on nonbipartite lattices exhibit an oscillatory imaginary phase known as the phase or sign problem, even at zero chemical potential. One method to alleviate the sign problem is to analytically continue the integration region of the state variables into the complex plane via holomorphic flow equations. For asymptotically large flow times, the state variables approach manifolds of constant imaginary phase known as Lefschetz thimbles. Furthermore, flowing such variables and calculating the ensuing Jacobian is a computationally demanding procedure. In this paper, we demonstrate that neural networks can be trained to parametrize suitable manifolds for this class of sign problem and drastically reduce the computational cost for different severely afflicted small volume systems. In particular, we apply our method to the Hubbard model on the triangle and tetrahedron, both of which are nonbipartite. At strong interaction strengths and modest temperatures, the tetrahedron suffers from a severe sign problem that cannot be overcome with standard reweighting techniques, while it quickly yields to our method. We benchmark our results with exact calculations and comment on future directions of this work.

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Research Organization:: Univ. of Maryland, College Park, MD (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-93ER40762

OSTI ID:: 1850040

Journal Information:: Physical Review. B, Vol. 103, Issue 12; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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