Fast and stable determinant quantum Monte Carlo

Abstract

We assess numerical stabilization methods employed in fermion many-body quantum Monte Carlo simulations. In particular, we empirically compare various matrix decomposition and inversion schemes to gain control over numerical instabilities arising in the computation of equal-time and time-displaced Green's functions within the determinant quantum Monte Carlo (DQMC) framework. Based on this comparison, we identify a procedure based on pivoted QR decompositions which is both efficient and accurate to machine precision. The Julia programming language is used for the assessment and implementations of all discussed algorithms are provided in the open-source software library StableDQMC.jl [http://github.com/crstnbr/StableDQMC.jl].

arXiv comment21 pages, 8 figures; minor fix

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Cited by in corpus (4)

• SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions (version 2.0 release)
• A flexible class of exact Hubbard-Stratonovich transformations
• The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code
• Quantum Transport Theory of Strongly Correlated Matter