Deconvolving the components of the sign problem

Journal Article · 04 January 2022 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.105.045107 · OSTI ID:1979715

Tarat, S. ^[1]; Xiao, Bo ^[2]; Mondaini, R.  ^[3]; Scalettar, R. T. ^[4]

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1. Beijing Computational Science Research Center, Beijing (China); OSTI
2. Flatiron Institute, New York, NY (United States)
3. Beijing Computational Science Research Center, Beijing (China)
4. University of California, Davis, CA (United States)

Auxiliary field quantum Monte Carlo simulations of interacting fermions require sampling over a Hubbard-Stratonovich field h introduced to decouple the interactions. The weight for a given configuration involves the products of the determinant of matrices $$M_σ(h)$$ where σ labels the species, and hence is typically not positive definite. Indeed, the average sign $$\langle \mathscr {L} \rangle$$ of the determinants goes to zero exponentially with increasing spatial size and decreasing temperature for most Hamiltonians of interest. This statement, however, does not explicitly separate two possible origins for the vanishing of $$\langle \mathscr {L} \rangle$$. Does $$\langle \mathscr {L} \rangle$$ → 0 because randomly chosen field configurations have det[M(h)] < 0, or does the sign problem arise because the specific subset of configurations chosen by the weighting function have a greater preponderance of negative values? In the latter case, the process of weighting the configurations with |det[M(h)]| might steer the simulation to a region of configuration space of h where positive and negative determinants are equally likely, even though randomly chosen h would preferentially have determinants with a single dominant sign. Here in this paper, we address the relative importance of these two mechanisms for the vanishing of $$\langle \mathscr {L} \rangle$$ in quantum simulations.

• Research Organization: University of California, Davis, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC); National Natural Science Foundation of China (NSFC); Flatiron Institute; Simons Foundation
• Grant/Contract Number: SC0014671
• OSTI ID: 1979715
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 4 Vol. 105; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English