Fast and stable determinant quantum Monte Carlo

Bauer, Carsten

doi:10.21468/SciPostPhysCore.2.2.011

SciPost Physics Core

Fast and stable determinant quantum Monte Carlo

Carsten Bauer

SciPost Phys. Core 2, 011 (2020) · published 29 June 2020

doi: 10.21468/SciPostPhysCore.2.2.011
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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].

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.2.2.011
TI  - Fast and stable determinant quantum Monte Carlo
PY  - 2020/06/29
UR  - https://scipost.org/SciPostPhysCore.2.2.011
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 2
IS  - 2
SP  - 011
A1  - Bauer, Carsten
AB  - 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].
ER  -

@Article{10.21468/SciPostPhysCore.2.2.011,
	title={{Fast and stable determinant quantum Monte Carlo}},
	author={Carsten Bauer},
	journal={SciPost Phys. Core},
	volume={2},
	pages={011},
	year={2020},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.2.2.011},
	url={https://scipost.org/10.21468/SciPostPhysCore.2.2.011},
}

Cited by 3

Ontology / Topics

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Quantum Monte Carlo simulations Quantum many-body systems

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¹ Carsten Bauer

¹ Universität zu Köln / University of Cologne [UoC]

Funder for the research work leading to this publication

Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]