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Title: Lefschetz thimble quantum Monte Carlo for spin systems

Abstract

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 problemmore » in spin coherent state path integral Monte Carlo enables a novel numerical demonstration of a breakdown in the spin coherent path integral.« less

Authors:
ORCiD logo [1]; ORCiD logo [1];  [2];  [3]
+ Show Author Affiliations
  1. NIST/University of Maryland, College Park, MD (United States)
  2. University of Washington, Seattle, WA (United States)
  3. NASA Ames Research Center, Moffett Field, CA (United States); KBR, Houston, TX (United States)
Publication Date:
Research Org.:
Univ. of Washington, Seattle, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)
OSTI Identifier:
2246658
Grant/Contract Number:  
FG02-00ER41132; NSF PHY-1748958; SC0020312; SC0019040
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. B
Additional Journal Information:
Journal Volume: 106; Journal Issue: 21; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Quantum computation; Path-integral Monte Carlo; Quantum Monte Carlo

Citation Formats

Mooney, T. C., Bringewatt, Jacob, Warrington, Neill C., and Brady, Lucas T. Lefschetz thimble quantum Monte Carlo for spin systems. United States: N. p., 2022. Web. doi:10.1103/physrevb.106.214416.
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Mooney, T. C., Bringewatt, Jacob, Warrington, Neill C., & Brady, Lucas T. Lefschetz thimble quantum Monte Carlo for spin systems. United States. https://doi.org/10.1103/physrevb.106.214416
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Mooney, T. C., Bringewatt, Jacob, Warrington, Neill C., and Brady, Lucas T. Thu . "Lefschetz thimble quantum Monte Carlo for spin systems". United States. https://doi.org/10.1103/physrevb.106.214416. https://www.osti.gov/servlets/purl/2246658.
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@article{osti_2246658,
title = {Lefschetz thimble quantum Monte Carlo for spin systems},
author = {Mooney, T. C. and Bringewatt, Jacob and Warrington, Neill C. and Brady, Lucas T.},
abstractNote = {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.},
doi = {10.1103/physrevb.106.214416},
journal = {Physical Review. B},
number = 21,
volume = 106,
place = {United States},
year = {Thu Dec 15 00:00:00 EST 2022},
month = {Thu Dec 15 00:00:00 EST 2022}
}
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https://doi.org/10.1103/physrevb.106.214416
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