Journal article
The Sign Problem in Density Matrix Quantum Monte Carlo
Journal of chemical theory and computation, Vol.17(10), pp.6036-6052
09/21/2021
DOI: 10.1021/acs.jctc.1c00078
Appears in UI Libraries Support Open Access
Abstract
Density matrix quantum Monte Carlo (DMQMC) is a recently developed method for stochastically sampling the N-particle thermal density matrix to obtain exact-on-average energies for model and ab initio systems. We report a systematic numerical study of the sign problem in DMQMC based on simulations of atomic and molecular systems. In DMQMC, the density matrix is written in an outer product basis of Slater determinants. In principle, this means that DMQMC needs to sample a space that scales in the system size, N, as O[(exp(N))2]. In practice, removing the sign problem requires a total walker population that exceeds a system-dependent critical walker population (Nc), imposing limitations on both storage and compute time. We establish that Nc for DMQMC is the square of Nc for FCIQMC. By contrast, the minimum Nc in the interaction picture modification of DMQMC (IP-DMQMC) is only linearly related to the Nc for FCIQMC. We find that this difference originates from the difference in propagation of IP-DMQMC versus canonical DMQMC: the former is asymmetric, whereas the latter is symmetric. When an asymmetric mode of propagation is used in DMQMC, there is a much greater stochastic error and is thus prohibitively expensive for DMQMC without the interaction picture adaptation. Finally, we find that the equivalence between IP-DMQMC and FCIQMC seems to extend to the initiator approximation, which is often required to study larger systems with large basis sets. This suggests that IP-DMQMC offers a way to ameliorate the cost of moving between a Slater determinant space and an outer product basis.
Details
- Title: Subtitle
- The Sign Problem in Density Matrix Quantum Monte Carlo
- Creators
- Hayley R Petras - Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1294, United StatesWilliam Z Van Benschoten - Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1294, United StatesSai Kumar Ramadugu - Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1294, United StatesJames J Shepherd - Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1294, United States] (ORCID:000000026164485X
- Resource Type
- Journal article
- Publication Details
- Journal of chemical theory and computation, Vol.17(10), pp.6036-6052
- DOI
- 10.1021/acs.jctc.1c00078
- ISSN
- 1549-9618
- eISSN
- 1549-9626
- Publisher
- American Chemical Society
- Grant note
- DOI: 10.13039/100006151, name: Basic Energy Sciences, award: DE-SC0021317; DOI: 10.13039/100008893, name: University of Iowa
- Language
- English
- Date published
- 09/21/2021
- Academic Unit
- Chemistry; ITS Research Services
- Record Identifier
- 9984176823302771
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