skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories

Journal Article · · Physical Review D

We show that standard identities and theorems for lattice models with U(1) symmetry get reexpressed discretely in the tensorial formulation of these models. We also explain the geometrical analogy between the continuous lattice equations of motion and the discrete selection rules of the tensors. We further construct a gauge-invariant transfer matrix in arbitrary dimensions, show the equivalence with its gauge-fixed version in a maximal temporal gauge, and explain how a discrete Gauss’s law is always enforced. Moreover, we propose a noise-robust way to implement Gauss’s law in arbitrary dimensions, and we reformulate Noether’s theorem for global, local, continuous, or discrete Abelian symmetries: for each given symmetry, there is one corresponding tensor redundancy. We discuss semiclassical approximations for classical solutions with periodic boundary conditions in two solvable cases, and we show the correspondence of their weak coupling limit with the tensor formulation after Poisson summation. Finally, we briefly discuss connections with other approaches and implications for quantum computing.

Research Organization:
Univ. of Iowa, Iowa City, IA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP)
Grant/Contract Number:
SC0010113; SC0019139
OSTI ID:
1638422
Alternate ID(s):
OSTI ID: 1656886
Journal Information:
Physical Review D, Journal Name: Physical Review D Vol. 102 Journal Issue: 1; ISSN 2470-0010
Publisher:
American Physical SocietyCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 7 works
Citation information provided by
Web of Science

References (65)

Order and disorder in gauge systems and magnets journal May 1978
Real-time dynamics and proposal for feasible experiments of lattice gauge–Higgs model simulated by cold atoms journal June 2015
Corner Transfer Matrix Renormalization Group Method journal April 1996
Accurate exponents from approximate tensor renormalizations journal February 2013
Tensor network formulation of the massless Schwinger model with staggered fermions journal May 2020
Tensor network analysis of critical coupling in two dimensional ϕ4 theory journal May 2019
The mass spectrum of the Schwinger model with matrix product states journal November 2013
Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O ( 2 ) sigma model journal June 2010
Critical behavior of the lattice Schwinger model with a topological term at θ = π using the Grassmann tensor renormalization group journal October 2014
Three-dimensional finite temperature Z2 gauge theory with tensor network scheme journal August 2019
Optical Abelian lattice gauge theories journal March 2013
Strong-coupling calculations of lattice gauge theories: (1 + 1)-dimensional exercises journal February 1976
Grassmann tensor renormalization group for the one-flavor lattice Gross–Neveu model with finite chemical potential journal April 2015
Controlling sign problems in spin models using tensor renormalization journal January 2014
Tensor renormalization group study of classical X Y model on the square lattice journal January 2014
The lattice gauge theory approach to quantum chromodynamics journal July 1983
Tensor Network Renormalization journal October 2015
Gauging Quantum States: From Global to Local Symmetries in Many-Body Systems journal February 2015
U(1) lattice gauge theory with a topological action journal June 2015
Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion journal February 2018
Tensor network formulation for two-dimensional lattice N $$ \mathcal{N} $$ = 1 Wess-Zumino model journal March 2018
Dual simulation of the 2d U(1) gauge Higgs model at topological angle θ = π: Critical endpoint behavior journal October 2018
Abelian gauge theories on the lattice: θ-Terms and compact gauge theory with(out) monopoles journal June 2019
Coarse-graining renormalization by higher-order singular value decomposition journal July 2012
Phase transitions in Z n gauge models: Towards quantum simulations of the Schwinger-Weyl QED journal October 2018
Lattice Gauge Theories and String Dynamics in Rydberg Atom Quantum Simulators journal May 2020
Digitizing gauge fields: Lattice Monte Carlo results for future quantum computers journal June 2019
Gauge-invariant implementation of the Abelian-Higgs model on optical lattices journal October 2015
Atomic Quantum Simulation of the Lattice Gauge-Higgs Model: Higgs Couplings and Emergence of Exact Local Gauge Symmetry journal September 2013
Tensor Networks for Lattice Gauge Theories with Continuous Groups journal November 2014
Dual simulation of the two-dimensional lattice U(1) gauge-Higgs model with a topological term journal December 2015
Real-space renormalization in statistical mechanics journal May 2014
Faster methods for contracting infinite two-dimensional tensor networks journal December 2018
General methods for digital quantum simulation of gauge theories journal August 2019
Second Renormalization of Tensor-Network States journal October 2009
Tensor renormalization group algorithms with a projective truncation method journal April 2019
Examples of renormalization group transformations for image sets journal November 2018
Die Vollst�ndigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe journal December 1927
Emerging Two-Dimensional Gauge Theories in Rydberg Configurable Arrays journal June 2020
Duality in field theory and statistical systems journal April 1980
Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order journal October 2009
Exact blocking formulas for spin and gauge models journal September 2013
An introduction to lattice gauge theory and spin systems journal October 1979
Quantum simulation of the Schwinger model: A study of feasibility journal October 2014
Oracles for Gauss's law on digital quantum computers journal April 2019
Progress towards quantum simulating the classical O ( 2 ) model journal December 2014
Gluon field digitization for quantum computers journal December 2019
Simulating Compact Quantum Electrodynamics with Ultracold Atoms: Probing Confinement and Nonperturbative Effects journal September 2012
Calculation of fermionic Green functions with Grassmann higher-order tensor renormalization group journal March 2018
Investigation of Complex ϕ4 Theory at Finite Density in Two Dimensions Using TRG journal February 2020
Density matrix renormalization group approach to the massive Schwinger model journal July 2002
Gauge fields on a lattice. III. Strong-coupling expansions and transition points journal April 1975
Tensor renormalization group study of the non-Abelian Higgs model in two dimensions journal June 2019
Gauge-invariant rotor Hamiltonian from dual variables of 3D U ( 1 ) gauge theory journal April 2019
Examples of symmetry-preserving truncations in tensor field theory journal July 2019
Renormalization Group Flows of Hamiltonians Using Tensor Networks journal June 2017
Universal features of the Abelian Polyakov loop in 1 + 1 dimensions journal November 2018
Real Time Dynamics and Confinement in the Z n Schwinger-Weyl lattice model for 1+1 QED journal June 2020
Tensor Renormalization Group Approach to Two-Dimensional Classical Lattice Models journal September 2007
Quantum Simulation of the Universal Features of the Polyakov Loop journal November 2018
QCD as a quantum link model journal September 1999
Parton physics on a quantum computer journal March 2020
Confinement and String Breaking for QED 2 in the Hamiltonian Picture journal November 2016
Worm Algorithms for Classical Statistical Models journal September 2001
Quantum link models: A discrete approach to gauge theories journal May 1997

Similar Records

Quantum Simulation of the Universal Features of the Polyakov Loop
Journal Article · Wed Nov 28 00:00:00 EST 2018 · Physical Review Letters · OSTI ID:1638422
+3 more
Examples of symmetry-preserving truncations in tensor field theory
Journal Article · Wed Jul 10 00:00:00 EDT 2019 · Physical Review. D. · OSTI ID:1638422
Tensor lattice field theory with applications to the renormalization group and quantum computing
Journal Article · Tue Oct 13 00:00:00 EDT 2020 · TBD · OSTI ID:1638422

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Lattice gauge theory
Symmetries
Quantum computing