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@ARTICLE{Gntgen:1019467,
      author       = {Gäntgen, Christoph and Berkowitz, Evan and Luu, Tom and
                      Ostmeyer, Johann and Rodekamp, Marcel},
      title        = {{F}ermionic {S}ign {P}roblem {M}inimization by {C}onstant
                      {P}ath {I}ntegral {C}ontour {S}hifts},
      reportid     = {FZJ-2023-05414, arXiv:2307.06785},
      year         = {2023},
      abstract     = {The path integral formulation of quantum mechanical
                      problems including fermions is often affected by a severe
                      numerical sign problem. We show how such a sign problem can
                      be alleviated by a judiciously chosen constant imaginary
                      offset to the path integral. Such integration contour
                      deformations introduce no additional computational cost to
                      the Hybrid Monte Carlo algorithm, while its effective sample
                      size is greatly increased. This makes otherwise unviable
                      simulations efficient for a wide range of parameters.
                      Applying our method to the Hubbard model, we find that the
                      sign problem is significantly reduced. Furthermore, we prove
                      that it vanishes completely for large chemical potentials, a
                      regime where the sign problem is expected to be particularly
                      severe without imaginary offsets. In addition to a numerical
                      analysis of such optimized contour shifts, we analytically
                      compute the shifts corresponding to the leading and
                      next-to-leading order corrections to the action. We find
                      that such simple approximations, free of significant
                      computational cost, suffice in many cases.},
      cin          = {IAS-4 / IKP-3 / CASA / JSC},
      cid          = {I:(DE-Juel1)IAS-4-20090406 / I:(DE-Juel1)VDB25 /
                      I:(DE-Juel1)CASA-20230315 / I:(DE-Juel1)JSC-20090406},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511) / DFG project
                      196253076 - TRR 110: Symmetrien und Strukturbildung in der
                      Quantenchromodynamik (196253076)},
      pid          = {G:(DE-HGF)POF4-5111 / G:(GEPRIS)196253076},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2307.06785},
      howpublished = {arXiv:2307.06785},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2307.06785;\%\%$},
      doi          = {10.34734/FZJ-2023-05414},
      url          = {https://juser.fz-juelich.de/record/1019467},
}