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@ARTICLE{Wynen:872981,
      author       = {Wynen, Jan-Lukas and Berkowitz, Evan and Körber,
                      Christopher and Lähde, Timo A. and Luu, Tom},
      title        = {{A}voiding ergodicity problems in lattice discretizations
                      of the {H}ubbard model},
      journal      = {Physical review / B},
      volume       = {100},
      number       = {7},
      issn         = {0163-1829},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2020-00438},
      pages        = {075141},
      year         = {2019},
      abstract     = {The Hubbard model arises naturally when electron-electron
                      interactions are added to the tight-binding descriptions of
                      many condensed matter systems. For instance, the
                      two-dimensional Hubbardmodel on the honeycomb lattice is
                      central to the ab initio description of the electronic
                      structure ofcarbon nanomaterials, such as graphene. Such
                      low-dimensional Hubbard models are advantageouslystudied
                      with Markov chain Monte Carlo methods, such as Hybrid Monte
                      Carlo (HMC). HMC is thestandard algorithm of the lattice
                      gauge theory community, as it is well suited to theories of
                      dynamicalfermions. As HMC performs continuous, global
                      updates of the lattice degrees of freedom, it
                      providessuperior scaling with system size relative to local
                      updating methods. A potential drawback of HMCis its
                      susceptibility to ergodicity problems due to so-called
                      exceptional configurations, for which thefermion operator
                      cannot be inverted. Recently, ergodicity problems were found
                      in some formulationsof HMC simulations of the Hubbard model.
                      Here, we address this issue directly and clarify underwhat
                      conditions ergodicity is maintained or violated in HMC
                      simulations of the Hubbard model.We study different lattice
                      formulations of the fermion operator and provide explicit,
                      representativecalculations for small systems, often
                      comparing to exact results. We show that a fermion
                      operatorcan be found which is both computationally
                      convenient and free of ergodicity problems.},
      cin          = {IAS-4 / IKP-3 / JARA-HPC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IAS-4-20090406 / I:(DE-Juel1)IKP-3-20111104 /
                      $I:(DE-82)080012_20140620$},
      pnm          = {574 - Theory, modelling and simulation (POF3-574) / Carbon
                      Nano-Structures with High-Performance Computing
                      $(jjsc37_20180501)$},
      pid          = {G:(DE-HGF)POF3-574 / $G:(DE-Juel1)jjsc37_20180501$},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000482213800001},
      doi          = {10.1103/PhysRevB.100.075141},
      url          = {https://juser.fz-juelich.de/record/872981},
}