Finite-density Monte Carlo calculations on sign-optimized manifolds

doi:10.1103/PhysRevD.97.094510

Title: Finite-density Monte Carlo calculations on sign-optimized manifolds

Abstract

We present a general technique for addressing sign problems that arise in Monte Carlo simulations of field theories. This method deforms the domain of the path integral to a manifold in complex field space that maximizes the average sign (therefore reducing the sign problem) within a parametrized family of manifolds. We presents results for the 1 + 1 dimensional Thirring model with Wilson fermions on lattice sizes up to 40 × 10. This method reaches higher μ than previous techniques while substantially decreasing the computational time required.

Authors:: Alexandru, Andrei; Bedaque, Paulo F.; Lamm, Henry; Lawrence, Scott

Publication Date:: 2018-05-31

Research Org.:: Univ. of Maryland, College Park, MD (United States); George Washington Univ., Washington, DC (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1439896

Alternate Identifier(s):: OSTI ID: 1498927

Grant/Contract Number:: FG02-95ER40907; FG02-93ER40762

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 9; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Alexandru, Andrei, Bedaque, Paulo F., Lamm, Henry, and Lawrence, Scott. Finite-density Monte Carlo calculations on sign-optimized manifolds.  United States: N. p., 2018. 
        Web.  doi:10.1103/PhysRevD.97.094510.

Copy to clipboard


                    Alexandru, Andrei, Bedaque, Paulo F., Lamm, Henry, & Lawrence, Scott. Finite-density Monte Carlo calculations on sign-optimized manifolds.  United States.  doi:https://doi.org/10.1103/PhysRevD.97.094510

Copy to clipboard


                    Alexandru, Andrei, Bedaque, Paulo F., Lamm, Henry, and Lawrence, Scott. Thu .  
        "Finite-density Monte Carlo calculations on sign-optimized manifolds".  United States.  doi:https://doi.org/10.1103/PhysRevD.97.094510.

Copy to clipboard


                    
@article{osti_1439896,

  title        = {Finite-density Monte Carlo calculations on sign-optimized manifolds},

  author       = {Alexandru, Andrei and Bedaque, Paulo F. and Lamm, Henry and Lawrence, Scott},

  abstractNote = {We present a general technique for addressing sign problems that arise in Monte Carlo simulations of field theories. This method deforms the domain of the path integral to a manifold in complex field space that maximizes the average sign (therefore reducing the sign problem) within a parametrized family of manifolds. We presents results for the 1 + 1 dimensional Thirring model with Wilson fermions on lattice sizes up to 40 × 10. This method reaches higher μ than previous techniques while substantially decreasing the computational time required.},

  doi          = {10.1103/PhysRevD.97.094510},

  journal      = {Physical Review D},

  number       = 9,

  volume       = 97,

  place        = {United States},

  year         = {2018},

  month        = {5}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Publisher's Version of Record
DOI: https://doi.org/10.1103/PhysRevD.97.094510

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 10 works

Citation information provided by
Web of Science

Figures / Tables:

Figure 1: Manifold parameters as a function of chemical potential μ/mf, for both 20 × 10 and 40 × 10 lattices, with bare parameters m = −0.25 and g = 1.

All figures and tables (3 total)

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Tempered transitions between thimbles
journal, August 2017

Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F.
Physical Review D, Vol. 96, Issue 3
DOI: 10.1103/PhysRevD.96.034513

Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
journal, January 2016

Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo
Physical Review D, Vol. 93, Issue 1
DOI: 10.1103/PhysRevD.93.014504

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

Tanizaki, Yuya; Hidaka, Yoshimasa; Hayata, Tomoya
New Journal of Physics, Vol. 18, Issue 3
DOI: 10.1088/1367-2630/18/3/033002

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

Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F.
Physical Review D, Vol. 93, Issue 9
DOI: 10.1103/PhysRevD.93.094514

Monte Carlo Study of Real Time Dynamics on the Lattice
journal, August 2016

Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F.
Physical Review Letters, Vol. 117, Issue 8
DOI: 10.1103/PhysRevLett.117.081602

QCD thermal phase transition in the presence of a small chemical potential
journal, October 2002

Allton, C. R.; Ejiri, S.; Hands, S. J.
Physical Review D, Vol. 66, Issue 7
DOI: 10.1103/PhysRevD.66.074507

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

Functional Integrals for QCD at Nonzero Chemical Potential and Zero Density
journal, November 2003

Cohen, Thomas D.
Physical Review Letters, Vol. 91, Issue 22
DOI: 10.1103/PhysRevLett.91.222001

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

Kanazawa, Takuya; Tanizaki, Yuya
Journal of High Energy Physics, Vol. 2015, Issue 3
DOI: 10.1007/JHEP03(2015)044

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

Mori, Yuto; Kashiwa, Kouji; Ohnishi, Akira
Physical Review D, Vol. 96, Issue 11
DOI: 10.1103/PhysRevD.96.111501

Fermion bag approach to fermion sign problems: New opportunities in lattice fermion field theories
journal, July 2013

Chandrasekharan, Shailesh
The European Physical Journal A, Vol. 49, Issue 7
DOI: 10.1140/epja/i2013-13090-y

Deep learning beyond Lefschetz thimbles
journal, November 2017

Alexandru, Andrei; Bedaque, Paulo F.; Lamm, Henry
Physical Review D, Vol. 96, Issue 9
DOI: 10.1103/PhysRevD.96.094505

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

Tanizaki, Yuya; Tachibana, Motoi
Journal of High Energy Physics, Vol. 2017, Issue 2
DOI: 10.1007/JHEP02(2017)081

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

Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F.
Physical Review D, Vol. 95, Issue 1
DOI: 10.1103/PhysRevD.95.014502

A new method to study lattice QCD at finite temperature and chemical potential
journal, May 2002

Fodor, Z.; Katz, S. D.
Physics Letters B, Vol. 534, Issue 1-4
DOI: 10.1016/S0370-2693(02)01583-6

Stochastic quantization at finite chemical potential
journal, September 2008

Aarts, Gert; Stamatescu, Ion-Olimpiu
Journal of High Energy Physics, Vol. 2008, Issue 09
DOI: 10.1088/1126-6708/2008/09/018

Erratum to: Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density
journal, September 2016

Fujii, Hirotsugu; Kamata, Syo; Kikukawa, Yoshio
Journal of High Energy Physics, Vol. 2016, Issue 9
DOI: 10.1007/JHEP09(2016)172

Thimble regularization at work: From toy models to chiral random matrix theories
journal, October 2015

Di Renzo, F.; Eruzzi, G.
Physical Review D, Vol. 92, Issue 8
DOI: 10.1103/PhysRevD.92.085030

Gauge and matter fields as surfaces and loops: An exploratory lattice study of the $Z_{3}$ gauge-Higgs model
journal, November 2012

Gattringer, Christof; Schmidt, Alexander
Physical Review D, Vol. 86, Issue 9
DOI: 10.1103/PhysRevD.86.094506

Metropolis Monte Carlo integration on the Lefschetz thimble: Application to a one-plaquette model
journal, September 2013

Mukherjee, Abhishek; Cristoforetti, Marco; Scorzato, Luigi
Physical Review D, Vol. 88, Issue 5
DOI: 10.1103/PhysRevD.88.051502

Finite density QCD with a canonical approach
journal, March 2006

de Forcrand, Philippe; Kratochvila, Slavo
Nuclear Physics B - Proceedings Supplements, Vol. 153, Issue 1
DOI: 10.1016/j.nuclphysbps.2006.01.007

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

Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F.
Physical Review D, Vol. 95, Issue 11
DOI: 10.1103/PhysRevD.95.114501

An efficient method to compute the residual phase on a Lefschetz thimble
journal, June 2014

Cristoforetti, M.; Di Renzo, F.; Eruzzi, G.
Physical Review D, Vol. 89, Issue 11
DOI: 10.1103/PhysRevD.89.114505

Hamilton dynamics for Lefschetz-thimble integration akin to the complex Langevin method
journal, September 2015

Fukushima, K.; Tanizaki, Y.
Progress of Theoretical and Experimental Physics, Vol. 2015, Issue 11
DOI: 10.1093/ptep/ptv152

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

Cristoforetti, Marco; Di Renzo, Francesco; Scorzato, Luigi
Physical Review D, Vol. 86, Issue 7
DOI: 10.1103/PhysRevD.86.074506

Lattice QCD at finite density via a new canonical approach
journal, December 2005

Alexandru, Andrei; Faber, Manfried; Horváth, Ivan
Physical Review D, Vol. 72, Issue 11
DOI: 10.1103/PhysRevD.72.114513

Study of symmetry breaking in a relativistic Bose gas using the contraction algorithm
journal, August 2016

Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo
Physical Review D, Vol. 94, Issue 4
DOI: 10.1103/PhysRevD.94.045017

The chiral critical line of N _f = 2+1 QCD at zero and non-zero baryon density
journal, January 2007

Forcrand, Philippe de; Philipsen, Owe
Journal of High Energy Physics, Vol. 2007, Issue 01
DOI: 10.1088/1126-6708/2007/01/077

From the Density-of-states Method to Finite Density Quantum Field Theory
journal, January 2016

Langfeld, K.; Lucini, B.
Acta Physica Polonica B Proceedings Supplement, Vol. 9, Issue 3
DOI: 10.5506/APhysPolBSupp.9.503

Figures / Tables found in this record:

Figure 1 (p. 5)

Figure 2 (p. 5)

Figure 3 (p. 6)

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

Similar Records in DOE PAGES and OSTI.GOV collections:

Fermions at Finite Density in $2 + 1$ Dimensions with Sign-Optimized Manifolds

Journal Article Alexandru, Andrei ; Bedaque, Paulo F. ; Lamm, Henry ; ... - Physical Review Letters

We present Monte Carlo calculations of the thermodynamics of the (2 + 1)-dimensional Thirring model at finite density. We bypass the sign problem by deforming the domain of integration of the path integral into complex space in such a way as to maximize the average sign within a parameterized family of manifolds. We present results for lattice sizes up to 10³ and we find that at high densities and/or temperatures the chiral condensate is abruptly reduced.
Cited by 3
DOI: https://doi.org/10.1103/PhysRevLett.121.191602
Sign problem and Monte Carlo calculations beyond Lefschetz thimbles

Journal Article Alexandru, Andrei ; Basar, Gokce ; Bedaque, Paulo F. ; ... - Journal of High Energy Physics (Online)

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 amore »« less
Cited by 15
DOI: https://doi.org/10.1007/JHEP05(2016)053

Full Text Available
Going with the flow: a new solution to the sign problem

Journal Article Başar, Gökçe - Nuclear Physics. A

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 asmore »« less
DOI: https://doi.org/10.1016/j.nuclphysa.2017.05.004

Full Text Available
Finite density ${QED}_{1 + 1}$ near Lefschetz thimbles

Journal Article Alexandru, Andrei ; Başar, Gökçe ; Bedaque, Paulo F. ; ... - Physical Review D

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 effortmore » than standard methods.« less
Cited by 4
DOI: https://doi.org/10.1103/PhysRevD.98.034506
Perturbative removal of a sign problem

Journal Article Lawrence, Scott - Physical Review D

This paper presents a method for alleviating sign problems in lattice path integrals, including those associated with finite fermion density in relativistic systems. The method makes use of information gained from some systematic expansion—such as perturbation theory—in order to accelerate the Monte Carlo computation. The method is exact, in the sense that no approximation to the lattice path integral is introduced. Thanks to the underlying systematic expansion, the method is systematically improvable, so that an arbitrary reduction in the sign problem can in principle be obtained. The Thirring model (in 0+1 and 1+1 dimensions) is used to demonstrate the abilitymore »« less
DOI: https://doi.org/10.1103/physrevd.102.094504

Full Text Available

Similar Records

Title: Finite-density Monte Carlo calculations on sign-optimized manifolds

Abstract

Citation Formats

Figures / Tables:

Tempered transitions between thimbles journal, August 2017

Monte Carlo algorithm for simulating fermions on Lefschetz thimbles journal, January 2016

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

Monte Carlo Study of Real Time Dynamics on the Lattice journal, August 2016

QCD thermal phase transition in the presence of a small chemical potential journal, October 2002

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

Functional Integrals for QCD at Nonzero Chemical Potential and Zero Density journal, November 2003

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

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

Fermion bag approach to fermion sign problems: New opportunities in lattice fermion field theories journal, July 2013

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

A new method to study lattice QCD at finite temperature and chemical potential journal, May 2002

Stochastic quantization at finite chemical potential journal, September 2008

Erratum to: Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density journal, September 2016

Thimble regularization at work: From toy models to chiral random matrix theories journal, October 2015

Gauge and matter fields as surfaces and loops: An exploratory lattice study of the Z 3 gauge-Higgs model journal, November 2012

Metropolis Monte Carlo integration on the Lefschetz thimble: Application to a one-plaquette model journal, September 2013

Finite density QCD with a canonical approach journal, March 2006

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

An efficient method to compute the residual phase on a Lefschetz thimble journal, June 2014

Hamilton dynamics for Lefschetz-thimble integration akin to the complex Langevin method journal, September 2015

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

Lattice QCD at finite density via a new canonical approach journal, December 2005

Study of symmetry breaking in a relativistic Bose gas using the contraction algorithm journal, August 2016

The chiral critical line of N f = 2+1 QCD at zero and non-zero baryon density journal, January 2007

From the Density-of-states Method to Finite Density Quantum Field Theory journal, January 2016

Tempered transitions between thimbles
journal, August 2017

Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
journal, January 2016

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

Monte Carlo Study of Real Time Dynamics on the Lattice
journal, August 2016

QCD thermal phase transition in the presence of a small chemical potential
journal, October 2002

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

Functional Integrals for QCD at Nonzero Chemical Potential and Zero Density
journal, November 2003

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

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

Fermion bag approach to fermion sign problems: New opportunities in lattice fermion field theories
journal, July 2013

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

A new method to study lattice QCD at finite temperature and chemical potential
journal, May 2002

Stochastic quantization at finite chemical potential
journal, September 2008

Erratum to: Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density
journal, September 2016

Thimble regularization at work: From toy models to chiral random matrix theories
journal, October 2015

Gauge and matter fields as surfaces and loops: An exploratory lattice study of the $Z_{3}$ gauge-Higgs model
journal, November 2012

Metropolis Monte Carlo integration on the Lefschetz thimble: Application to a one-plaquette model
journal, September 2013

Finite density QCD with a canonical approach
journal, March 2006

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

An efficient method to compute the residual phase on a Lefschetz thimble
journal, June 2014

Hamilton dynamics for Lefschetz-thimble integration akin to the complex Langevin method
journal, September 2015

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

Lattice QCD at finite density via a new canonical approach
journal, December 2005

Study of symmetry breaking in a relativistic Bose gas using the contraction algorithm
journal, August 2016

The chiral critical line of N _f = 2+1 QCD at zero and non-zero baryon density
journal, January 2007

From the Density-of-states Method to Finite Density Quantum Field Theory
journal, January 2016