Sampling using SU ( N ) gauge equivariant flows

Boyda, Denis; Kanwar, Gurtej; Racanière, Sébastien; Rezende, Danilo Jimenez; Albergo, Michael S.; Cranmer, Kyle; Hackett, Daniel C.; Shanahan, Phiala E.

doi:10.1103/PhysRevD.103.074504

Title: Sampling using $SU (N)$ gauge equivariant flows

Abstract

We develop a flow-based sampling algorithm for SU(N) lattice gauge theories that is gauge invariant by construction. Our key contribution is constructing a class of flows on an SU(N) variable [or on a U(N) variable by a simple alternative] that respects matrix conjugation symmetry. We apply this technique to sample distributions of single SU(N) variables and to construct flow-based samplers for SU(2) and SU(3) lattice gauge theory in two dimensions.

Authors:

;

; Racanière, Sébastien;

;

; Cranmer, Kyle;

; Shanahan, Phiala E.

Publication Date:: Tue Apr 20 00:00:00 EDT 2021

Research Org.:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); National Science Foundation (NSF); NEC; Carl G and Shirley Sontheimer; Moore-Sloan Data Science; Carl Feinberg Fellowship in Theoretical Physics

OSTI Identifier:: 1779319

Alternate Identifier(s):: OSTI ID: 1851472; OSTI ID: 1991371

Grant/Contract Number:: SC0011090; AC02-06CH11357; SC0021006; 1841699; 2035015; ACI-1450310; OAC1836650; OAC-1841471; PHY-2019786

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 103 Journal Issue: 7; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 79 ASTRONOMY AND ASTROPHYSICS; astronomy & astrophysics; physics; lattice QCD; strong interaction; quantum chromodynamics; lattice field theory; quantum field theory; symmetries in condensed matter; gauge symmetries; Monte Carlo methods

Citation Formats


                    Boyda, Denis, Kanwar, Gurtej, Racanière, Sébastien, Rezende, Danilo Jimenez, Albergo, Michael S., Cranmer, Kyle, Hackett, Daniel C., and Shanahan, Phiala E. Sampling using SU ( N ) gauge equivariant flows.  United States: N. p., 2021. 
Web.  doi:10.1103/PhysRevD.103.074504.

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                    Boyda, Denis, Kanwar, Gurtej, Racanière, Sébastien, Rezende, Danilo Jimenez, Albergo, Michael S., Cranmer, Kyle, Hackett, Daniel C., & Shanahan, Phiala E. Sampling using SU ( N ) gauge equivariant flows.  United States.  https://doi.org/10.1103/PhysRevD.103.074504

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                    Boyda, Denis, Kanwar, Gurtej, Racanière, Sébastien, Rezende, Danilo Jimenez, Albergo, Michael S., Cranmer, Kyle, Hackett, Daniel C., and Shanahan, Phiala E. Tue .  
"Sampling using SU ( N ) gauge equivariant flows".  United States.  https://doi.org/10.1103/PhysRevD.103.074504.

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@article{osti_1779319,

  title        = {Sampling using SU ( N ) gauge equivariant flows},

  author       = {Boyda, Denis and Kanwar, Gurtej and Racanière, Sébastien and Rezende, Danilo Jimenez and Albergo, Michael S. and Cranmer, Kyle and Hackett, Daniel C. and Shanahan, Phiala E.},

  abstractNote = {We develop a flow-based sampling algorithm for SU(N) lattice gauge theories that is gauge invariant by construction. Our key contribution is constructing a class of flows on an SU(N) variable [or on a U(N) variable by a simple alternative] that respects matrix conjugation symmetry. We apply this technique to sample distributions of single SU(N) variables and to construct flow-based samplers for SU(2) and SU(3) lattice gauge theory in two dimensions.},

  doi          = {10.1103/PhysRevD.103.074504},

  journal      = {Physical Review D},

  number       = 7,

  volume       = 103,

  place        = {United States},

  year         = {Tue Apr 20 00:00:00 EDT 2021},

  month        = {Tue Apr 20 00:00:00 EDT 2021}

}

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Title: Sampling using SU ( N ) gauge equivariant flows

Abstract

Citation Formats

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Title: Sampling using $SU (N)$ gauge equivariant flows

Topological order, emergent gauge fields, and Fermi surface reconstruction
journal, November 2018

Equivariant Flow-Based Sampling for Lattice Gauge Theory
journal, September 2020

Regressive and generative neural networks for scalar field theory
journal, July 2019

Brane dynamics and gauge theory
journal, July 1999

Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning
journal, September 2019

Erratum to “Monte Carlo errors with less errors” [Comput. Phys. Comm. 156 (2004) 143–153]
journal, March 2007

Enhanced thermal Hall effect in the square-lattice Néel state
journal, October 2019

Energy flow networks: deep sets for particle jets
journal, January 2019

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journal, January 2004

Gauge fixing, the transfer matrix, and confinement on a lattice
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Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models
journal, January 2021

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Adventure in Topological Phase Transitions in $3 + 1$ -D: Non-Abelian Deconfined Quantum Criticalities and a Possible Duality
journal, May 2019

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