Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories

Raychowdhury, Indrakshi; Stryker, Jesse R.

doi:10.1103/PhysRevD.101.114502

Title: Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories

Abstract

The question of how to efficiently formulate Hamiltonian gauge theories is experiencing renewed interest due to advances in building quantum simulation platforms. We introduce a reformulation of an SU(2) Hamiltonian lattice gauge theory—a loop-string-hadron (LSH) formulation—that describes dynamics directly in terms of its loop, string, and hadron degrees of freedom, while alleviating several disadvantages of quantum simulating the Kogut-Susskind formulation. This LSH formulation transcends the local loop formulation of $$\textit{d}$$ + 1-dimensional lattice gauge theories by incorporating staggered quarks, furnishing the algebra of gauge-singlet operators, and being used to reconstruct dynamics between states that have Gauss’s law built in to them. LSH operators are then factored into products of “normalized” ladder operators and diagonal matrices, priming them for classical or quantum information processing. Self-contained expressions of the Hamiltonian are given up to $$\textit{d}$$ = 3. The LSH formalism makes little use of structures specific to SU(2), and its conceptual clarity makes it an attractive approach to apply to other non-Abelian groups like SU(3).

Authors:: Raychowdhury, Indrakshi; Stryker, Jesse R.

Publication Date:: Mon Jun 08 00:00:00 EDT 2020

Research Org.:: Univ. of Washington, Seattle, WA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)

OSTI Identifier:: 1632733

Alternate Identifier(s):: OSTI ID: 1799986

Grant/Contract Number:: FG02-00ER41132; 1256082

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 11; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Astronomy & Astrophysics; Physics

Citation Formats


                    Raychowdhury, Indrakshi, and Stryker, Jesse R. Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevD.101.114502.

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                    Raychowdhury, Indrakshi, & Stryker, Jesse R. Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories.  United States.  https://doi.org/10.1103/PhysRevD.101.114502

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                    Raychowdhury, Indrakshi, and Stryker, Jesse R. Mon .  
"Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories".  United States.  https://doi.org/10.1103/PhysRevD.101.114502.

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@article{osti_1632733,

  title        = {Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories},

  author       = {Raychowdhury, Indrakshi and Stryker, Jesse R.},

  abstractNote = {The question of how to efficiently formulate Hamiltonian gauge theories is experiencing renewed interest due to advances in building quantum simulation platforms. We introduce a reformulation of an SU(2) Hamiltonian lattice gauge theory—a loop-string-hadron (LSH) formulation—that describes dynamics directly in terms of its loop, string, and hadron degrees of freedom, while alleviating several disadvantages of quantum simulating the Kogut-Susskind formulation. This LSH formulation transcends the local loop formulation of $\textit{d}$ + 1-dimensional lattice gauge theories by incorporating staggered quarks, furnishing the algebra of gauge-singlet operators, and being used to reconstruct dynamics between states that have Gauss’s law built in to them. LSH operators are then factored into products of “normalized” ladder operators and diagonal matrices, priming them for classical or quantum information processing. Self-contained expressions of the Hamiltonian are given up to $\textit{d}$ = 3. The LSH formalism makes little use of structures specific to SU(2), and its conceptual clarity makes it an attractive approach to apply to other non-Abelian groups like SU(3).},

  doi          = {10.1103/PhysRevD.101.114502},

  journal      = {Physical Review D},

  number       = 11,

  volume       = 101,

  place        = {United States},

  year         = {Mon Jun 08 00:00:00 EDT 2020},

  month        = {Mon Jun 08 00:00:00 EDT 2020}

}

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Title: Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories

Abstract

Citation Formats

Mass gap in the weak coupling limit of ( 2 + 1 )-dimensional SU(2) lattice gauge theory journal, April 2018

Harmonic oscillator pre-potentials in SU (2) lattice gauge theory journal, November 2005

Prepotential formulation of SU (3) lattice gauge theory journal, December 2009

Equation of state and QCD transition at finite temperature journal, July 2009

Freeze-Out Parameters: Lattice Meets Experiment journal, August 2013

Proton-Proton Fusion and Tritium β Decay from Lattice Quantum Chromodynamics journal, August 2017

Atomic Quantum Simulation of Dynamical Gauge Fields Coupled to Fermionic Matter: From String Breaking to Evolution after a Quench journal, October 2012

Double- β decay matrix elements from lattice quantum chromodynamics journal, September 2017

Atomic Quantum Simulation of U ( N ) and SU ( N ) Non-Abelian Lattice Gauge Theories journal, March 2013

Cold-Atom Quantum Simulator for SU(2) Yang-Mills Lattice Gauge Theory journal, March 2013

Floquet approach to ℤ2 lattice gauge theories with ultracold atoms in optical lattices journal, September 2019

Ultraviolet Behavior of Non-Abelian Gauge Theories journal, June 1973

Reliable Perturbative Results for Strong Interactions? journal, June 1973

2 + 1 flavor lattice QCD toward the physical point journal, February 2009

Quantum-classical computation of Schwinger model dynamics using quantum computers journal, September 2018

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

Twenty-First Century Lattice Gauge Theory: Results from the Quantum Chromodynamics Lagrangian journal, November 2012

Hamiltonian formulation of Wilson's lattice gauge theories journal, January 1975

Simulating lattice gauge theories on a quantum computer journal, February 2006

Local observables in non-abelian gauge theories journal, March 1982

Solution of the SU(2) Mandelstam constraints journal, March 1994

SU(N) irreducible Schwinger bosons journal, September 2010

Loop approach to lattice gauge theories journal, September 2007

Heavy baryon spectroscopy from the lattice journal, September 1996

Digital Quantum Simulation of Z 2 Lattice Gauge Theories with Dynamical Fermionic Matter journal, February 2017

General methods for digital quantum simulation of gauge theories journal, August 2019

Irreducible SU(3) Schwinger bosons journal, May 2009

U(1) Wilson lattice gauge theories in digital quantum simulators journal, October 2017

SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers journal, April 2020

On the product of semi-groups of operators journal, April 1959

Low energy spectrum of SU(2) lattice gauge theory: An alternate proposal via loop formulation journal, March 2019

SU(2) lattice gauge theory: Local dynamics on nonintersecting electric flux loops journal, December 2014

Towards analog quantum simulations of lattice gauge theories with trapped ions journal, April 2020

Approaches to the sign problem in lattice field theory journal, August 2016

Generalized Trotter's formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems journal, June 1976

Real-time dynamics of lattice gauge theories with a few-qubit quantum computer journal, June 2016

Simulation of non-Abelian gauge theories with optical lattices journal, October 2013

Confinement of quarks journal, October 1974

Gluon field digitization for quantum computers journal, December 2019

Charge-monopole duality and the phases of non-Abelian gauge theories journal, April 1979

Loop states in lattice gauge theory journal, September 2006

Quantum supremacy using a programmable superconducting processor journal, October 2019

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories journal, July 2013

The QCD transition temperature: results with physical masses in the continuum limit II journal, June 2009

Doping a Mott insulator: Physics of high-temperature superconductivity journal, January 2006

Yang-Mills theory without Mandelstam constraints journal, July 1993

Towards quantum simulating QCD journal, November 2014

Mass gap in the weak coupling limit of ( $2 + 1$ )-dimensional SU(2) lattice gauge theory
journal, April 2018

Harmonic oscillator pre-potentials in SU (2) lattice gauge theory
journal, November 2005

Prepotential formulation of SU (3) lattice gauge theory
journal, December 2009

Equation of state and QCD transition at finite temperature
journal, July 2009

Freeze-Out Parameters: Lattice Meets Experiment
journal, August 2013

Proton-Proton Fusion and Tritium $β$ Decay from Lattice Quantum Chromodynamics
journal, August 2017

Atomic Quantum Simulation of Dynamical Gauge Fields Coupled to Fermionic Matter: From String Breaking to Evolution after a Quench
journal, October 2012

Double- $β$ decay matrix elements from lattice quantum chromodynamics
journal, September 2017

Atomic Quantum Simulation of $U (N)$ and $SU (N)$ Non-Abelian Lattice Gauge Theories
journal, March 2013

Cold-Atom Quantum Simulator for SU(2) Yang-Mills Lattice Gauge Theory
journal, March 2013

Floquet approach to ℤ2 lattice gauge theories with ultracold atoms in optical lattices
journal, September 2019

Ultraviolet Behavior of Non-Abelian Gauge Theories
journal, June 1973

Reliable Perturbative Results for Strong Interactions?
journal, June 1973

$2 + 1$ flavor lattice QCD toward the physical point
journal, February 2009

Quantum-classical computation of Schwinger model dynamics using quantum computers
journal, September 2018

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

Twenty-First Century Lattice Gauge Theory: Results from the Quantum Chromodynamics Lagrangian
journal, November 2012

Hamiltonian formulation of Wilson's lattice gauge theories
journal, January 1975

Simulating lattice gauge theories on a quantum computer
journal, February 2006

Local observables in non-abelian gauge theories
journal, March 1982

Solution of the SU(2) Mandelstam constraints
journal, March 1994

SU(N) irreducible Schwinger bosons
journal, September 2010

Loop approach to lattice gauge theories
journal, September 2007

Heavy baryon spectroscopy from the lattice
journal, September 1996

Digital Quantum Simulation of $Z_{2}$ Lattice Gauge Theories with Dynamical Fermionic Matter
journal, February 2017

General methods for digital quantum simulation of gauge theories
journal, August 2019

Irreducible SU(3) Schwinger bosons
journal, May 2009

U(1) Wilson lattice gauge theories in digital quantum simulators
journal, October 2017

SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers
journal, April 2020

On the product of semi-groups of operators
journal, April 1959

Low energy spectrum of SU(2) lattice gauge theory: An alternate proposal via loop formulation
journal, March 2019

SU(2) lattice gauge theory: Local dynamics on nonintersecting electric flux loops
journal, December 2014

Towards analog quantum simulations of lattice gauge theories with trapped ions
journal, April 2020

Approaches to the sign problem in lattice field theory
journal, August 2016

Generalized Trotter's formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems
journal, June 1976

Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
journal, June 2016

Simulation of non-Abelian gauge theories with optical lattices
journal, October 2013

Confinement of quarks
journal, October 1974

Gluon field digitization for quantum computers
journal, December 2019

Charge-monopole duality and the phases of non-Abelian gauge theories
journal, April 1979

Loop states in lattice gauge theory
journal, September 2006

Quantum supremacy using a programmable superconducting processor
journal, October 2019

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories
journal, July 2013

The QCD transition temperature: results with physical masses in the continuum limit II
journal, June 2009

Doping a Mott insulator: Physics of high-temperature superconductivity
journal, January 2006

Yang-Mills theory without Mandelstam constraints
journal, July 1993

Towards quantum simulating QCD
journal, November 2014