Importance-sampling FCIQMC: Solving weak sign-problem systems

We investigate the exact full configuration interaction quantum Monte Carlo algorithm (without the initiator approximation) applied to weak sign-problem fermionic systems, namely, systems in which the energy gap to the corresponding sign-free or “stoquastized” state is small. We show that the minimu...

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Veröffentlicht in:The Journal of chemical physics 2022-09, Vol.157 (12), p.124111-124111
Hauptverfasser: Liebermann, Niklas, Ghanem, Khaldoon, Alavi, Ali
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Sprache:eng
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Zusammenfassung:We investigate the exact full configuration interaction quantum Monte Carlo algorithm (without the initiator approximation) applied to weak sign-problem fermionic systems, namely, systems in which the energy gap to the corresponding sign-free or “stoquastized” state is small. We show that the minimum number of walkers required to exactly overcome the sign problem can be significantly reduced via an importance-sampling similarity transformation even though the similarity-transformed Hamiltonian has the same stoquastic gap as the untransformed one. Furthermore, we show that in the off-half-filling Hubbard model at U/t = 8, the real-space (site) representation has a much weaker sign problem compared to the momentum space representation. By applying importance sampling using a Gutzwiller-like guiding wavefunction, we are able to substantially reduce the minimum number of walkers in the case of 2 × ℓ Hubbard ladders, enabling us to get exact energies for sizable ladders. With these results, we calculate the fundamental charge gap ΔEfund = E(N + 1) + E(N − 1) − 2E(N) for the ladder systems compared to strictly one-dimensional Hubbard chains and show that the ladder systems have a reduced fundamental gap compared to the 1D chains.
ISSN:0021-9606
1089-7690
DOI:10.1063/5.0107317