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The Hubbard model arises naturally when electron-electron interactions areadded to the tight-binding descriptions of many condensed matter systems. Forinstance, the two-dimensional Hubbard model on the honeycomb lattice is centralto the ab initio description of the electronic structure of carbonnanomaterials, such as graphene. Such low-dimensional Hubbard models areadvantageously studied with Markov chain Monte Carlo methods, such as HybridMonte Carlo (HMC). HMC is the standard algorithm of the lattice gauge theorycommunity, as it is well suited to theories of dynamical fermions. As HMCperforms continuous, global updates of the lattice degrees of freedom, itprovides superior scaling with system size relative to local updating methods.A potential drawback of HMC is its susceptibility to ergodicity problems due toso-called exceptional configurations, for which the fermion operator cannot beinverted. Recently, ergodicity problems were found in some formulations of HMCsimulations of the Hubbard model. Here, we address this issue directly andclarify under what conditions ergodicity is maintained or violated in HMCsimulations of the Hubbard model. We study different lattice formulations ofthe fermion operator and provide explicit, representative calculations forsmall systems, often comparing to exact results. We show that a fermionoperator can be found which is both computationally convenient and free ofergodicity problems.

Avoiding Ergodicity Problems in Lattice Discretizations of the Hubbard Model