Lefschetz thimble quantum Monte Carlo for spin systems
- NIST/University of Maryland, College Park, MD (United States)
- University of Washington, Seattle, WA (United States)
- NASA Ames Research Center, Moffett Field, CA (United States); KBR, Houston, TX (United States)
Monte Carlo simulations are useful tools for modeling quantum systems, but in some cases they suffer from a sign problem, leading to an exponential slow down in their convergence to a value. While solving the sign problem is generically NP hard, many techniques exist for mitigating the sign problem in specific cases; in particular, the technique of deforming the Monte Carlo simulation's plane of integration onto Lefschetz thimbles (complex hypersurfaces of stationary phase) has seen significant success in the context of quantum field theories. We extend this methodology to spin systems by utilizing spin coherent state path integrals to reexpress the spin system's partition function in terms of continuous variables. Using some toy systems, we demonstrate its effectiveness at lessening the sign problem in this setting, despite the fact that the initial mapping to spin coherent states introduces its own sign problem. The standard formulation of the spin coherent path integral is known to make use of uncontrolled approximations; despite this, for large spins they are typically considered to yield accurate results, so it is somewhat surprising that our results show significant systematic errors. Furthermore, possibly of independent interest, our use of Lefschetz thimbles to overcome the intrinsic sign problem in spin coherent state path integral Monte Carlo enables a novel numerical demonstration of a breakdown in the spin coherent path integral.
- Research Organization:
- Univ. of Washington, Seattle, WA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)
- Grant/Contract Number:
- FG02-00ER41132; NSF PHY-1748958; SC0020312; SC0019040
- OSTI ID:
- 2246658
- Journal Information:
- Physical Review. B, Vol. 106, Issue 21; ISSN 2469-9950
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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