Journal Article

FZJ-2020-00438

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Avoiding ergodicity problems in lattice discretizations of the Hubbard model

Wynen, J.-L. (Corresponding author)FZJ* ; Berkowitz, E.FZJ* ; Körber, C.Extern*FZJ* ; Lähde, T. A.FZJ* ; Luu, T.FZJ*

2019
Inst. Woodbury, NY

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Please use a persistent id in citations: http://hdl.handle.net/2128/24177  doi:10.1103/PhysRevB.100.075141

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.

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Contributing Institute(s):

1. Theorie der Starken Wechselwirkung (IAS-4)
2. Theorie der starken Wechselwirkung (IKP-3)
3. JARA - HPC (JARA-HPC)

Research Program(s):

1. 574 - Theory, modelling and simulation (POF3-574) (POF3-574)
2. Carbon Nano-Structures with High-Performance Computing (jjsc37_20180501) (jjsc37_20180501)

Appears in the scientific report 2019

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Web of Science Core Collection

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