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000891466 1001_ $$0P:(DE-Juel1)171733$$aWynen, Jan-Lukas$$b0$$eCorresponding author
000891466 245__ $$aMachine learning to alleviate Hubbard-model sign problems
000891466 260__ $$aWoodbury, NY$$bInst.77671$$c2021
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000891466 520__ $$aLattice Monte Carlo calculations of interacting systems on non-bipartite lattices exhibit an oscillatory imaginary phase known as the phase or sign problem, even at zero chemical potential. One method to alleviate the sign problem is to analytically continue the integration region of the state variables into the complex plane via holomorphic flow equations. For asymptotically large flow times the state variables approach manifolds of constant imaginary phase known as Lefschetz thimbles. However, flowing such variables and calculating the ensuing Jacobian is a computationally demanding procedure. In this paper we demonstrate that neural networks can be trained to parameterize suitable manifolds for this class of sign problem and drastically reduce the computational cost. We apply our method to the Hubbard model on the triangle and tetrahedron, both of which are non-bipartite. At strong interaction strengths and modest temperatures the tetrahedron suffers from a severe sign problem that cannot be overcome with standard reweighting techniques, while it quickly yields to our method. We benchmark our results with exact calculations and comment on future directions of this work.
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000891466 7001_ $$0P:(DE-Juel1)171536$$aBerkowitz, Evan$$b1
000891466 7001_ $$0P:(DE-Juel1)132171$$aKrieg, Stefan$$b2
000891466 7001_ $$0P:(DE-Juel1)159481$$aLuu, Thomas$$b3
000891466 7001_ $$0P:(DE-HGF)0$$aOstmeyer, Johann$$b4
000891466 773__ $$0PERI:(DE-600)2844160-6$$a10.1103/PhysRevB.103.125153$$gVol. 103, no. 12, p. 125153$$n12$$p125153$$tPhysical review / B$$v103$$x2469-9969$$y2021
000891466 8564_ $$uhttps://arxiv.org/abs/2006.11221
000891466 8564_ $$uhttps://juser.fz-juelich.de/record/891466/files/PhysRevB.103.125153.pdf$$yOpenAccess
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