TY  - JOUR
AU  - Wynen, Jan-Lukas
AU  - Berkowitz, Evan
AU  - Körber, Christopher
AU  - Lähde, Timo A.
AU  - Luu, Tom
TI  - Avoiding ergodicity problems in lattice discretizations of the Hubbard model
JO  - Physical review / B
VL  - 100
IS  - 7
SN  - 0163-1829
CY  - Woodbury, NY
PB  - Inst.
M1  - FZJ-2020-00438
SP  - 075141
PY  - 2019
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000482213800001
DO  - DOI:10.1103/PhysRevB.100.075141
UR  - https://juser.fz-juelich.de/record/872981
ER  -