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@ARTICLE{Wynen:891466,
      author       = {Wynen, Jan-Lukas and Berkowitz, Evan and Krieg, Stefan and
                      Luu, Thomas and Ostmeyer, Johann},
      title        = {{M}achine learning to alleviate {H}ubbard-model sign
                      problems},
      journal      = {Physical review / B},
      volume       = {103},
      number       = {12},
      issn         = {2469-9969},
      address      = {Woodbury, NY},
      publisher    = {Inst.77671},
      reportid     = {FZJ-2021-01548},
      pages        = {125153},
      year         = {2021},
      abstract     = {Lattice 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.},
      cin          = {JSC / IAS-4},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JSC-20090406 / I:(DE-Juel1)IAS-4-20090406},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5111},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000646187300005},
      doi          = {10.1103/PhysRevB.103.125153},
      url          = {https://juser.fz-juelich.de/record/891466},
}