Sign problem and Monte Carlo calculations beyond Lefschetz thimbles
Abstract
We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action (“Lefschetz thimble”). We describe a family of such manifolds that interpolate between the tangent space at one critical point (where the sign problem is milder compared to the real plane but in some cases still severe) and the union of relevant thimbles (where the sign problem is mild but a multimodal distribution function complicates the Monte Carlo sampling). As a result, we exemplify this approach using a simple 0+1 dimensional fermion model previously used on sign problem studies and show that it can solve the model for some parameter values where a solution using Lefschetz thimbles was elusive.
- Authors:
-
- The George Washington Univ., Washington, D.C. (United States)
- Univ. of Maryland, College Park, MD (United States)
- Publication Date:
- Research Org.:
- Univ. of Maryland, College Park, MD (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1326947
- Grant/Contract Number:
- FG02-93ER40762
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 5; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice Quantum Field Theory; Nonperturbative Effects
Citation Formats
Alexandru, Andrei, Basar, Gokce, Bedaque, Paulo F., Ridgway, Gregory W., and Warrington, Neill C. Sign problem and Monte Carlo calculations beyond Lefschetz thimbles. United States: N. p., 2016.
Web. doi:10.1007/JHEP05(2016)053.
Alexandru, Andrei, Basar, Gokce, Bedaque, Paulo F., Ridgway, Gregory W., & Warrington, Neill C. Sign problem and Monte Carlo calculations beyond Lefschetz thimbles. United States. https://doi.org/10.1007/JHEP05(2016)053
Alexandru, Andrei, Basar, Gokce, Bedaque, Paulo F., Ridgway, Gregory W., and Warrington, Neill C. Tue .
"Sign problem and Monte Carlo calculations beyond Lefschetz thimbles". United States. https://doi.org/10.1007/JHEP05(2016)053. https://www.osti.gov/servlets/purl/1326947.
@article{osti_1326947,
title = {Sign problem and Monte Carlo calculations beyond Lefschetz thimbles},
author = {Alexandru, Andrei and Basar, Gokce and Bedaque, Paulo F. and Ridgway, Gregory W. and Warrington, Neill C.},
abstractNote = {We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action (“Lefschetz thimble”). We describe a family of such manifolds that interpolate between the tangent space at one critical point (where the sign problem is milder compared to the real plane but in some cases still severe) and the union of relevant thimbles (where the sign problem is mild but a multimodal distribution function complicates the Monte Carlo sampling). As a result, we exemplify this approach using a simple 0+1 dimensional fermion model previously used on sign problem studies and show that it can solve the model for some parameter values where a solution using Lefschetz thimbles was elusive.},
doi = {10.1007/JHEP05(2016)053},
journal = {Journal of High Energy Physics (Online)},
number = 5,
volume = 2016,
place = {United States},
year = {Tue May 10 00:00:00 EDT 2016},
month = {Tue May 10 00:00:00 EDT 2016}
}
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