Going with the flow: a new solution to the sign problem

Başar, Gökçe

doi:10.1016/j.nuclphysa.2017.05.004

Title: Going with the flow: a new solution to the sign problem

Abstract

Here, we discuss a novel solution for the sign problem which prevents first principle Monte-Carlo computations of QCD at finite chemical potential (especially important for both the search for the critical point and neutron star physics) as well as real time quantities such as transport coefficients. The solution is based on deforming the region of integration in the path integral into a complex manifold where the sign problem can be mitigated substantially. We explain the new Monte-Carlo algorithm based on this idea and give examples of interacting quantum field theories (bosonic and fermionic) with nonzero chemical potential as well as real time dynamics where this method successfully solves the sign problem. Furthermore this approach generalizes the ”Lefschetz thimble” method that received much attention lately. We also compare/contrast with the complex Langevin method.

Authors:

Başar, Gökçe ^[1]

Univ. of Illinois, Chicago, IL (United States)

Publication Date:: Mon Sep 25 00:00:00 EDT 2017

Research Org.:: Univ. of Illinois, Chicago, IL (United States); Univ. of Maryland, College Park, MD (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1502403

Grant/Contract Number:: FG02-01ER41195; FG02-93ER40762

Resource Type:: Accepted Manuscript

Journal Name:: Nuclear Physics. A

Additional Journal Information:: Journal Volume: 967; Journal Issue: C; Journal ID: ISSN 0375-9474

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; lattice field theory; sign problem; real time dynamics; finite density

Citation Formats


                    Başar, Gökçe. Going with the flow: a new solution to the sign problem.  United States: N. p., 2017. 
Web.  doi:10.1016/j.nuclphysa.2017.05.004.

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                    Başar, Gökçe. Going with the flow: a new solution to the sign problem.  United States.  https://doi.org/10.1016/j.nuclphysa.2017.05.004

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                    Başar, Gökçe. Mon .  
"Going with the flow: a new solution to the sign problem".  United States.  https://doi.org/10.1016/j.nuclphysa.2017.05.004.  https://www.osti.gov/servlets/purl/1502403.

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@article{osti_1502403,

  title        = {Going with the flow: a new solution to the sign problem},

  author       = {Başar, Gökçe},

  abstractNote = {Here, we discuss a novel solution for the sign problem which prevents first principle Monte-Carlo computations of QCD at finite chemical potential (especially important for both the search for the critical point and neutron star physics) as well as real time quantities such as transport coefficients. The solution is based on deforming the region of integration in the path integral into a complex manifold where the sign problem can be mitigated substantially. We explain the new Monte-Carlo algorithm based on this idea and give examples of interacting quantum field theories (bosonic and fermionic) with nonzero chemical potential as well as real time dynamics where this method successfully solves the sign problem. Furthermore this approach generalizes the ”Lefschetz thimble” method that received much attention lately. We also compare/contrast with the complex Langevin method.},

  doi          = {10.1016/j.nuclphysa.2017.05.004},

  journal      = {Nuclear Physics. A},

  number       = C,

  volume       = 967,

  place        = {United States},

  year         = {Mon Sep 25 00:00:00 EDT 2017},

  month        = {Mon Sep 25 00:00:00 EDT 2017}

}

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Journal Article:

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https://doi.org/10.1016/j.nuclphysa.2017.05.004

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Figures / Tables:

Fig. 1. : The discretized Schwinger-Keldysh contour (left) and the 〈T ẋ(t)ẋ(0)〉 correlator (right). The solid and dashed lines are the exact values computed numerically in the strongly coupled region. The parameters: $ω$ = 1, $λ$ = 24, $β$ = 0.8, $a$ = 1

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Fig. 1. (p. 3)

Fig. 2. (p. 4)

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