Gradient flows without blow-up for Lefschetz thimbles

Tanizaki, Yuya; Nishimura, Hiromichi; Verbaarschot, Jacobus J.  M.

doi:10.1007/JHEP10(2017)100

Title: Gradient flows without blow-up for Lefschetz thimbles

Abstract

We propose new gradient flows that define Lefschetz thimbles and do not blow up in a finite flow time. Here, we study analytic properties of these gradient flows, and confirm them by numerical tests in simple examples.

Authors:

^[1]; Nishimura, Hiromichi ^[1]; Verbaarschot, Jacobus J. M. ^[2]

Brookhaven National Lab. (BNL), Upton, NY (United States). RIKEN Research Center
Stony Brook Univ., NY (United States). Dept. of Physics and Astronomy

Publication Date:: 2017-10-16

Research Org.:: Brookhaven National Lab. (BNL), Upton, NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1425163

Report Number(s):: RBRC-1241; BNL-114873-2017-JAAM
Journal ID: ISSN 1029-8479; TRN: US1802056

Grant/Contract Number:: SC0012704

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: 2017; Journal Issue: 10; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Tanizaki, Yuya, Nishimura, Hiromichi, and Verbaarschot, Jacobus J.  M. Gradient flows without blow-up for Lefschetz thimbles.  United States: N. p., 2017. 
Web.  https://doi.org/10.1007/JHEP10(2017)100.

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                    Tanizaki, Yuya, Nishimura, Hiromichi, & Verbaarschot, Jacobus J.  M. Gradient flows without blow-up for Lefschetz thimbles.  United States.  https://doi.org/10.1007/JHEP10(2017)100

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                    Tanizaki, Yuya, Nishimura, Hiromichi, and Verbaarschot, Jacobus J.  M. Mon .  
"Gradient flows without blow-up for Lefschetz thimbles".  United States.  https://doi.org/10.1007/JHEP10(2017)100.  https://www.osti.gov/servlets/purl/1425163.

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@article{osti_1425163,

  title        = {Gradient flows without blow-up for Lefschetz thimbles},

  author       = {Tanizaki, Yuya and Nishimura, Hiromichi and Verbaarschot, Jacobus J.  M.},

  abstractNote = {We propose new gradient flows that define Lefschetz thimbles and do not blow up in a finite flow time. Here, we study analytic properties of these gradient flows, and confirm them by numerical tests in simple examples.},

  doi          = {10.1007/JHEP10(2017)100},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 10,

  volume       = 2017,

  place        = {United States},

  year         = {2017},

  month        = {10}

}

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Works referencing / citing this record:

Phase structure of the twisted SU(3)/U(1)2 flag sigma model on ℝ × S1
journal, February 2019

Hongo, Masaru; Misumi, Tatsuhiro; Tanizaki, Yuya
Journal of High Energy Physics, Vol. 2019, Issue 2
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Real-time quantum dynamics, path integrals and the method of thimbles
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Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles
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Mou, Zong-Gang; Saffin, Paul M.; Tranberg, Anders
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Review on novel methods for lattice gauge theories
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Carmen Bañuls, Mari; Cichy, Krzysztof
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Why is the mission impossible? Decoupling the mirror Ginsparg–Wilson fermions in the lattice models for two-dimensional Abelian chiral gauge theories
journal, July 2019

Kikukawa, Y.
Progress of Theoretical and Experimental Physics, Vol. 2019, Issue 7
DOI: 10.1093/ptep/ptz055

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Title: Gradient flows without blow-up for Lefschetz thimbles

Abstract

Citation Formats

RG flows and bifurcations journal, June 2017

Complex Langevin: etiology and diagnostics of its main problem journal, October 2011

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

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

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

Sign problem in the numerical simulation of many-electron systems journal, May 1990

Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD journal, August 2016

Lectures on non-perturbative effects in large N gauge theories, matrix models and strings: Non-perturbative effects in large N gauge theories, matrix models and strings journal, April 2014

Random Matrix Model of QCD at Finite Density and the Nature of the Quenched Limit journal, June 1996

Holomorphic matrix integrals journal, July 2004

Phase of the Fermion Determinant at Nonzero Chemical Potential journal, January 2007

No-Go Theorem for Critical Phenomena in Large- N c QCD journal, March 2012

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

Analytic continuation of Liouville theory journal, December 2011

Some remarks on Lefschetz thimbles and complex Langevin dynamics journal, October 2014

Recent developments in quantum Monte Carlo simulations with applications for cold gases journal, August 2012

Hyperasymptotics for multidimensional integrals, exact remainder terms and the global connection problem journal, November 1997

Resurgence and holomorphy: From weak to strong coupling journal, May 2015

Hidden Topological Angles in Path Integrals journal, July 2015

Resurgence theory, ghost-instantons, and analytic continuation of path integrals journal, October 2013

Orbifold Equivalence and the Sign Problem at Finite Baryon Density journal, March 2011

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

Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations journal, May 2005

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

Resurgence and trans-series in Quantum Field Theory: the $\mathbb{C}{{\mathbb{P}}^{N-1 }}$ model journal, November 2012

The fermion propagator matrix in lattice QCD journal, May 1986

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

Nonperturbative effects and nonperturbative definitions in matrix models and topological strings journal, December 2008

The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painlevé II Equation journal, April 2014

QCD sign problem for small chemical potential journal, June 2007

Global Symmetries, Volume Independence, and Continuity in Quantum Field Theories journal, January 2017

The curious incident of multi-instantons and the necessity of Lefschetz thimbles journal, November 2015

Neutral bions in the ℂ $$ \mathbb{C} $$ P N −1 model journal, June 2014

Path integrals in the theory of condensed helium journal, April 1995

The phase diagram of dense QCD journal, December 2010

Real-time Feynman path integral with Picard–Lefschetz theory and its applications to quantum tunneling journal, December 2014

Lattice Monte Carlo simulations of QCD at finite baryonic density journal, December 1986

Lattice QCD at Finite Density: An Introductory Review journal, October 2003

The critical points of strongly coupled lattice QCD at nonzero chemical potential journal, December 1997

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

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

Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles journal, October 2015

Resurgence and the Nekrasov-Shatashvili limit: connecting weak and strong coupling in the Mathieu and Lamé systems journal, February 2015

Complex saddle points and the sign problem in complex Langevin simulation journal, October 2016

Results on finite density QCD journal, January 1998

Phase structure of the twisted SU(3)/U(1)2 flag sigma model on ℝ × S1 journal, February 2019

Real-time quantum dynamics, path integrals and the method of thimbles journal, June 2019

Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles journal, November 2019

Review on novel methods for lattice gauge theories journal, January 2020

Why is the mission impossible? Decoupling the mirror Ginsparg–Wilson fermions in the lattice models for two-dimensional Abelian chiral gauge theories journal, July 2019

RG flows and bifurcations
journal, June 2017

Complex Langevin: etiology and diagnostics of its main problem
journal, October 2011

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

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

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

Sign problem in the numerical simulation of many-electron systems
journal, May 1990

Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD
journal, August 2016

Lectures on non-perturbative effects in large N gauge theories, matrix models and strings: Non-perturbative effects in large N gauge theories, matrix models and strings
journal, April 2014

Random Matrix Model of QCD at Finite Density and the Nature of the Quenched Limit
journal, June 1996

Holomorphic matrix integrals
journal, July 2004

Phase of the Fermion Determinant at Nonzero Chemical Potential
journal, January 2007

No-Go Theorem for Critical Phenomena in Large- $N_{c}$ QCD
journal, March 2012

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

Analytic continuation of Liouville theory
journal, December 2011

Some remarks on Lefschetz thimbles and complex Langevin dynamics
journal, October 2014

Recent developments in quantum Monte Carlo simulations with applications for cold gases
journal, August 2012

Hyperasymptotics for multidimensional integrals, exact remainder terms and the global connection problem
journal, November 1997

Resurgence and holomorphy: From weak to strong coupling
journal, May 2015

Hidden Topological Angles in Path Integrals
journal, July 2015

Resurgence theory, ghost-instantons, and analytic continuation of path integrals
journal, October 2013

Orbifold Equivalence and the Sign Problem at Finite Baryon Density
journal, March 2011

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

Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations
journal, May 2005

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

Resurgence and trans-series in Quantum Field Theory: the $\mathbb{C}{{\mathbb{P}}^{N-1 }}$ model
journal, November 2012

The fermion propagator matrix in lattice QCD
journal, May 1986

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

Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
journal, December 2008

The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painlevé II Equation
journal, April 2014

QCD sign problem for small chemical potential
journal, June 2007

Global Symmetries, Volume Independence, and Continuity in Quantum Field Theories
journal, January 2017

The curious incident of multi-instantons and the necessity of Lefschetz thimbles
journal, November 2015

Neutral bions in the ℂ $$ \mathbb{C} $$ P N −1 model
journal, June 2014

Path integrals in the theory of condensed helium
journal, April 1995

The phase diagram of dense QCD
journal, December 2010

Real-time Feynman path integral with Picard–Lefschetz theory and its applications to quantum tunneling
journal, December 2014

Lattice Monte Carlo simulations of QCD at finite baryonic density
journal, December 1986

Lattice QCD at Finite Density: An Introductory Review
journal, October 2003

The critical points of strongly coupled lattice QCD at nonzero chemical potential
journal, December 1997

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

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

Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
journal, October 2015

Resurgence and the Nekrasov-Shatashvili limit: connecting weak and strong coupling in the Mathieu and Lamé systems
journal, February 2015

Complex saddle points and the sign problem in complex Langevin simulation
journal, October 2016

Results on finite density QCD
journal, January 1998

Phase structure of the twisted SU(3)/U(1)2 flag sigma model on ℝ × S1
journal, February 2019

Real-time quantum dynamics, path integrals and the method of thimbles
journal, June 2019

Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles
journal, November 2019

Review on novel methods for lattice gauge theories
journal, January 2020

Why is the mission impossible? Decoupling the mirror Ginsparg–Wilson fermions in the lattice models for two-dimensional Abelian chiral gauge theories
journal, July 2019