Preprint
The sign problem in density matrix quantum Monte Carlo
ArXiv.org
01/29/2021
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 systemic numerical study 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 and has a size of space which is the square of the number of Slater determinants. In principle this means DMQMC needs to sample a space which scales in the system size, N, as O[(exp(N))2]. We find that, while DMQMC suffers a sign problem that scales with the size of the outer product space, the interaction picture modification of DMQMC (IP-DMQMC) has a sign problem which only scales with the size of original determinant space. We achieve this by establishing that the critical walker population to converge a simulation is the same between IP-DMQMC and full configuration interaction quantum Monte Carlo (FCIQMC). This equivalence between IP-DMQMC and FCIQMC seems to extend to the initiator approximation, which is often required to study larger basis sets and other systems. This suggests IP-DMQMC ameliorates 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 PetrasWilliam Z Van BenschotenSai Kumar RamaduguJames J Shepherd
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- ISSN
- 2331-8422
- Language
- English
- Date posted
- 01/29/2021
- Academic Unit
- Research Services; Chemistry
- Record Identifier
- 9984077788502771
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