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Title: Finite density QED 1 + 1 near Lefschetz thimbles

Abstract

One strategy for reducing the sign problem in finite-density field theories is to deform the path integral contour from real to complex fields. If the deformed manifold is the appropriate combination of Lefschetz thimbles—or somewhat close to them—the sign problem is alleviated. Gauge theories require generalizing the definition of thimble decompositions, and therefore it is unclear how to carry out a generalized thimble method. In this paper we discuss some of the conceptual issues involved by applying this method to QED 1 + 1 at finite density, showing that the generalized thimble method yields correct results with less computational effort than standard methods.

Authors:
; ; ; ;
Publication Date:
Research Org.:
Univ. of Illinois, Chicago, IL (United States); George Washington Univ., Washington, DC (United States); Univ. of Maryland, College Park, MD (United States)
Sponsoring Org.:
USDOE; National Science Foundation (NSF)
OSTI Identifier:
1467759
Alternate Identifier(s):
OSTI ID: 1498965
Grant/Contract Number:  
FG02-95ER40907; DE FG02-01ER41195; FG02-93ER-40762; FG02-01ER41195; FG02-93ER40762; PHY-1151648
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 3; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Alexandru, Andrei, Başar, Gökçe, Bedaque, Paulo F., Lamm, Henry, and Lawrence, Scott. Finite density QED 1 + 1 near Lefschetz thimbles. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.98.034506.
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Alexandru, Andrei, Başar, Gökçe, Bedaque, Paulo F., Lamm, Henry, & Lawrence, Scott. Finite density QED 1 + 1 near Lefschetz thimbles. United States. https://doi.org/10.1103/PhysRevD.98.034506
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Alexandru, Andrei, Başar, Gökçe, Bedaque, Paulo F., Lamm, Henry, and Lawrence, Scott. Thu . "Finite density QED 1 + 1 near Lefschetz thimbles". United States. https://doi.org/10.1103/PhysRevD.98.034506.
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@article{osti_1467759,
title = {Finite density QED 1 + 1 near Lefschetz thimbles},
author = {Alexandru, Andrei and Başar, Gökçe and Bedaque, Paulo F. and Lamm, Henry and Lawrence, Scott},
abstractNote = {One strategy for reducing the sign problem in finite-density field theories is to deform the path integral contour from real to complex fields. If the deformed manifold is the appropriate combination of Lefschetz thimbles—or somewhat close to them—the sign problem is alleviated. Gauge theories require generalizing the definition of thimble decompositions, and therefore it is unclear how to carry out a generalized thimble method. In this paper we discuss some of the conceptual issues involved by applying this method to QED 1 + 1 at finite density, showing that the generalized thimble method yields correct results with less computational effort than standard methods.},
doi = {10.1103/PhysRevD.98.034506},
journal = {Physical Review D},
number = 3,
volume = 98,
place = {United States},
year = {2018},
month = {8}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevD.98.034506
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Citation Metrics:
Cited by: 22 works
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Figures / Tables:

FIG. 1. FIG. 1.: A schematic view of Stokes’ phenomenon. The original integration contour is given by the dash-dotted green line. The solid dots denote the critical points, solid lines denote different thimbles, and the arrows denote the orientation of the thimbles. As the argument of S changes (from left to right),more » the thimble decomposition jumps from $T$ 1 (left) to $T$ 1 + $T$ 2 (right). When Stokes’ phenomenon occurs (center) there is no unique thimble decomposition, which we indicate by two paths of integration given by the red dashed and blue dotted lines.« less
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Works referenced in this record:

Tempered transitions between thimbles
journal, August 2017

Solving the sign problems of the massless lattice Schwinger model with a dual formulation
journal, August 2015

Lefschetz-thimble analysis of the sign problem in one-site fermion model
journal, March 2016

Fast estimator of Jacobians in the Monte Carlo integration on Lefschetz thimbles
journal, May 2016

Sign problem and Monte Carlo calculations beyond Lefschetz thimbles
journal, May 2016

  • Alexandru, Andrei; Basar, Gökçe; Bedaque, Paulo F.
  • Journal of High Energy Physics, Vol. 2016, Issue 5
  • DOI: 10.1007/JHEP05(2016)053

Structure of Lefschetz thimbles in simple fermionic systems
journal, March 2015

Toward solving the sign problem with path optimization method
journal, December 2017

Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
journal, February 2017

Deep learning beyond Lefschetz thimbles
journal, November 2017

Multi-flavor massless QED2 at finite densities via Lefschetz thimbles
journal, February 2017

Monte Carlo calculations of the finite density Thirring model
journal, January 2017

Parallel tempering algorithm for integration over Lefschetz thimbles
journal, July 2017

  • Fukuma, Masafumi; Umeda, Naoya
  • Progress of Theoretical and Experimental Physics, Vol. 2017, Issue 7
  • DOI: 10.1093/ptep/ptx081

Lefschetz-thimble techniques for path integral of zero-dimensional O ( n ) sigma models
journal, February 2015

Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
journal, November 2015

  • Fujii, Hirotsugu; Kamata, Syo; Kikukawa, Yoshio
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)078

Monte Carlo simulations on the Lefschetz thimble: Taming the sign problem
journal, September 2013

  • Cristoforetti, Marco; Di Renzo, Francesco; Mukherjee, Abhishek
  • Physical Review D, Vol. 88, Issue 5
  • DOI: 10.1103/PhysRevD.88.051501

Schwinger-Keldysh formalism on the lattice: A faster algorithm and its application to field theory
journal, June 2017

Finite-density Monte Carlo calculations on sign-optimized manifolds
journal, May 2018

Gradient flows without blow-up for Lefschetz thimbles
journal, October 2017

  • Tanizaki, Yuya; Nishimura, Hiromichi; Verbaarschot, Jacobus J. M.
  • Journal of High Energy Physics, Vol. 2017, Issue 10
  • DOI: 10.1007/JHEP10(2017)100

New approach to the sign problem in quantum field theories: High density QCD on a Lefschetz thimble
journal, October 2012

Combining the complex Langevin method and the generalized Lefschetz-thimble method
journal, June 2017

  • Nishimura, Jun; Shimasaki, Shinji
  • Journal of High Energy Physics, Vol. 2017, Issue 6
  • DOI: 10.1007/JHEP06(2017)023

Erratum to: Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
journal, February 2016

  • Fujii, Hirotsugu; Kamata, Syo; Kikukawa, Yoshio
  • Journal of High Energy Physics, Vol. 2016, Issue 2
  • DOI: 10.1007/JHEP02(2016)036

Hybrid Monte Carlo on Lefschetz thimbles — A study of the residual sign problem
journal, October 2013

Application of a neural network to the sign problem via the path optimization method
journal, February 2018

  • Mori, Yuto; Kashiwa, Kouji; Ohnishi, Akira
  • Progress of Theoretical and Experimental Physics, Vol. 2018, Issue 2
  • DOI: 10.1093/ptep/ptx191
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    Review on novel methods for lattice gauge theories
    journal, January 2020

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      Figures / Tables found in this record:

      FIG. 1. (p. 5)figure
      FIG. 2. (p. 6)figure
      TABLE I (p. 6)table
      FIG. 3. (p. 7)figure
      FIG. 4. (p. 7)figure
      FIG. 5. (p. 8)figure
      TABLE II (p. 8)table
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