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.  doi:10.1007/JHEP10(2017)100.

Copy to clipboard


                    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

Copy to clipboard


                    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.

Copy to clipboard


                    
@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}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1007/JHEP10(2017)100

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 16 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

RG flows and bifurcations
journal, June 2017

Gukov, Sergei
Nuclear Physics B, Vol. 919
DOI: 10.1016/j.nuclphysb.2017.03.025

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

Aarts, Gert; James, Frank A.; Seiler, Erhard
The European Physical Journal C, Vol. 71, Issue 10
DOI: 10.1140/epjc/s10052-011-1756-5

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

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

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

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

Cherman, Aleksey; Schäfer, Thomas; Ünsal, Mithat
Physical Review Letters, Vol. 117, Issue 8
DOI: 10.1103/PhysRevLett.117.081601

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

Mariño, M.
Fortschritte der Physik, Vol. 62, Issue 5-6
DOI: 10.1002/prop.201400005

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

Stephanov, M. A.
Physical Review Letters, Vol. 76, Issue 24
DOI: 10.1103/PhysRevLett.76.4472

Holomorphic matrix integrals
journal, July 2004

Felder, Giovanni; Riser, Roman
Nuclear Physics B, Vol. 691, Issue 3
DOI: 10.1016/j.nuclphysb.2004.05.010

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

Splittorff, K.; Verbaarschot, J. J. M.
Physical Review Letters, Vol. 98, Issue 3
DOI: 10.1103/PhysRevLett.98.031601

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

Hidaka, Yoshimasa; Yamamoto, Naoki
Physical Review Letters, Vol. 108, Issue 12
DOI: 10.1103/PhysRevLett.108.121601

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

Analytic continuation of Liouville theory
journal, December 2011

Harlow, Daniel; Maltz, Jonathan; Witten, Edward
Journal of High Energy Physics, Vol. 2011, Issue 12
DOI: 10.1007/JHEP12(2011)071

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

Aarts, Gert; Bongiovanni, Lorenzo; Seiler, Erhard
Journal of High Energy Physics, Vol. 2014, Issue 10
DOI: 10.1007/JHEP10(2014)159

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

Pollet, Lode
Reports on Progress in Physics, Vol. 75, Issue 9
DOI: 10.1088/0034-4885/75/9/094501

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

Howls, C. J.
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 453, Issue 1966
DOI: 10.1098/rspa.1997.0122

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

Cherman, Aleksey; Koroteev, Peter; Ünsal, Mithat
Journal of Mathematical Physics, Vol. 56, Issue 5
DOI: 10.1063/1.4921155

Hidden Topological Angles in Path Integrals
journal, July 2015

Behtash, Alireza; Sulejmanpasic, Tin; Schäfer, Thomas
Physical Review Letters, Vol. 115, Issue 4
DOI: 10.1103/PhysRevLett.115.041601

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

Basar, Gökçe; Dunne, Gerald V.; Ünsal, Mithat
Journal of High Energy Physics, Vol. 2013, Issue 10
DOI: 10.1007/JHEP10(2013)041

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

Cherman, Aleksey; Hanada, Masanori; Robles-Llana, Daniel
Physical Review Letters, Vol. 106, Issue 9
DOI: 10.1103/PhysRevLett.106.091603

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

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

Dunne, Gerald V.; Ünsal, Mithat
Journal of High Energy Physics, Vol. 2012, Issue 11
DOI: 10.1007/JHEP11(2012)170

The fermion propagator matrix in lattice QCD
journal, May 1986

Gibbs, P. E.
Physics Letters B, Vol. 172, Issue 1
DOI: 10.1016/0370-2693(86)90215-7

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

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

Mariño, Marcos
Journal of High Energy Physics, Vol. 2008, Issue 12
DOI: 10.1088/1126-6708/2008/12/114

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

Schiappa, Ricardo; Vaz, Ricardo
Communications in Mathematical Physics, Vol. 330, Issue 2
DOI: 10.1007/s00220-014-2028-7

QCD sign problem for small chemical potential
journal, June 2007

Splittorff, K.; Verbaarschot, J. J. M.
Physical Review D, Vol. 75, Issue 11
DOI: 10.1103/PhysRevD.75.116003

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

Sulejmanpasic, Tin
Physical Review Letters, Vol. 118, Issue 1
DOI: 10.1103/PhysRevLett.118.011601

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

Behtash, Alireza; Poppitz, Erich; Sulejmanpasic, Tin
Journal of High Energy Physics, Vol. 2015, Issue 11
DOI: 10.1007/JHEP11(2015)175

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

Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke
Journal of High Energy Physics, Vol. 2014, Issue 6
DOI: 10.1007/JHEP06(2014)164

The phase diagram of dense QCD
journal, December 2010

Fukushima, Kenji; Hatsuda, Tetsuo
Reports on Progress in Physics, Vol. 74, Issue 1
DOI: 10.1088/0034-4885/74/1/014001

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

Tanizaki, Yuya; Koike, Takayuki
Annals of Physics, Vol. 351
DOI: 10.1016/j.aop.2014.09.003

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

Gibbs, Philip E.
Physics Letters B, Vol. 182, Issue 3-4
DOI: 10.1016/0370-2693(86)90109-7

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

Muroya, S.; Nakamura, A.; Nonaka, C.
Progress of Theoretical Physics, Vol. 110, Issue 4
DOI: 10.1143/PTP.110.615

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

Barbour, Ian M.; Morrison, Susan E.; Klepfish, Elyakum G.
Physical Review D, Vol. 56, Issue 11
DOI: 10.1103/PhysRevD.56.7063

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

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

Fujii, H.; Honda, D.; Kato, M.
Journal of High Energy Physics, Vol. 2013, Issue 10
DOI: 10.1007/JHEP10(2013)147

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

Cherman, Aleksey; Dorigoni, Daniele; Ünsal, Mithat
Journal of High Energy Physics, Vol. 2015, Issue 10
DOI: 10.1007/JHEP10(2015)056

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

Basar, Gökçe; Dunne, Gerald V.
Journal of High Energy Physics, Vol. 2015, Issue 2
DOI: 10.1007/JHEP02(2015)160

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

Hayata, Tomoya; Hidaka, Yoshimasa; Tanizaki, Yuya
Nuclear Physics B, Vol. 911
DOI: 10.1016/j.nuclphysb.2016.07.031

Results on finite density QCD
journal, January 1998

Barbour, Ian M.; Morrison, Susan E.; Klepfish, Elyakum G.
Nuclear Physics B - Proceedings Supplements, Vol. 60, Issue 1-2
DOI: 10.1016/S0920-5632(97)00484-2

Works referencing / citing this record:

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

Mou, Zong-Gang; Saffin, Paul M.; Tranberg, Anders
Journal of High Energy Physics, Vol. 2019, Issue 6
DOI: 10.1007/jhep06(2019)094

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

Carmen Bañuls, Mari; Cichy, Krzysztof
Reports on Progress in Physics, Vol. 83, Issue 2
DOI: 10.1088/1361-6633/ab6311

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

Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
text, January 2017

Kikukawa, Yoshio
arXiv
DOI: 10.48550/arxiv.1710.11101

Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles
text, January 2019

Mou, Zong-Gang; Saffin, Paul M.; Tranberg, Anders
arXiv
DOI: 10.48550/arxiv.1909.02488

Review on novel methods for lattice gauge theories
text, January 2019

Bañuls, Mari Carmen; Cichy, Krzysztof
arXiv
DOI: 10.48550/arxiv.1910.00257

Similar Records in DOE PAGES and OSTI.GOV collections:

The curious incident of multi-instantons and the necessity of Lefschetz thimbles

Journal Article Behtash, Alireza ; Poppitz, Erich ; Sulejmanpasic, Tin ; ... - Journal of High Energy Physics (Online)

Here, we smore »« less
Cited by 27
https://doi.org/10.1007/JHEP11(2015)175

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 22
https://doi.org/10.1103/PhysRevD.98.034506
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 83
https://doi.org/10.1007/JHEP05(2016)053

Full Text Available
Normalizing flows and the real-time sign problem

Journal Article Lawrence, Scott ; Yamauchi, Yukari - Physical Review D

Normalizing flows have recently been applied to the problem of accelerating Markov chains in lattice field theory. We propose a generalization of normalizing flows that allows them to applied to theories with a sign problem. These complex normalizing flows are closely related to contour deformations (i.e., the generalized Lefschetz thimble method), which been applied to sign problems in the past. We discuss the question of the existence of normalizing flows; they do not exist in the most general case, but we argue that exact normalizing flows are likely to exist for many physically interesting problems, including cases where the Lefschetzmore »« less
https://doi.org/10.1103/PhysRevD.103.114509
Real-time Feynman path integral with Picard–Lefschetz theory and its applications to quantum tunneling

Journal Article Tanizaki, Yuya ; Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198 ; Koike, Takayuki - Annals of Physics (New York)

Picard–Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its computational method in a concrete way by solving three simple examples of quantum mechanics. It is applied to quantum mechanics of a double-well potential, and quantum tunneling is discussed. We identify all of the complex saddle points of the classical action, and their properties are discussed in detail. However a big theoretical difficulty turns out to appear in rewriting the original path integral into a sum of path integralsmore »« less
https://doi.org/10.1016/J.AOP.2014.09.003

Similar Records

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

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

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

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

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

Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories text, January 2017

Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles text, January 2019

Review on novel methods for lattice gauge theories text, January 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

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

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

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

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

Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
text, January 2017

Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles
text, January 2019

Review on novel methods for lattice gauge theories
text, January 2019