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Title: Examples of symmetry-preserving truncations in tensor field theory

Abstract

We consider the tensor formulation of the nonlinear O(2) sigma model and its gauged version (the compact Abelian Higgs model), on a D-dimensional cubic lattice, and show that tensorial truncations are compatible with the general identities derived from the symmetries of these models. This means that the universal properties of these models can be reproduced with highly simplified formulations desirable for implementations with quantum computers or for quantum simulations experiments. We discuss the extensions to global non-Abelian symmetries, discrete symmetries and pure gauge Abelian models.

Authors:
Publication Date:
Research Org.:
Univ. of Iowa, Iowa City, IA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1532789
Alternate Identifier(s):
OSTI ID: 1611360
Grant/Contract Number:  
SC0010113; SC0019139
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 1; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTRONOMY AND ASTROPHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Astronomy & Astrophysics; Physics

Citation Formats

Meurice, Yannick. Examples of symmetry-preserving truncations in tensor field theory. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.014506.
Meurice, Yannick. Examples of symmetry-preserving truncations in tensor field theory. United States. doi:10.1103/PhysRevD.100.014506.
Meurice, Yannick. Wed . "Examples of symmetry-preserving truncations in tensor field theory". United States. doi:10.1103/PhysRevD.100.014506.
@article{osti_1532789,
title = {Examples of symmetry-preserving truncations in tensor field theory},
author = {Meurice, Yannick},
abstractNote = {We consider the tensor formulation of the nonlinear O(2) sigma model and its gauged version (the compact Abelian Higgs model), on a D-dimensional cubic lattice, and show that tensorial truncations are compatible with the general identities derived from the symmetries of these models. This means that the universal properties of these models can be reproduced with highly simplified formulations desirable for implementations with quantum computers or for quantum simulations experiments. We discuss the extensions to global non-Abelian symmetries, discrete symmetries and pure gauge Abelian models.},
doi = {10.1103/PhysRevD.100.014506},
journal = {Physical Review D},
number = 1,
volume = 100,
place = {United States},
year = {2019},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.100.014506

Citation Metrics:
Cited by: 3 works
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Works referenced in this record:

Corner Transfer Matrix Renormalization Group Method
journal, April 1996

  • Nishino, Tomotoshi; Okunishi, Kouichi
  • Journal of the Physical Society of Japan, Vol. 65, Issue 4
  • DOI: 10.1143/JPSJ.65.891

Accurate exponents from approximate tensor renormalizations
journal, February 2013


Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O ( 2 ) sigma model
journal, June 2010


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


Grassmann tensor renormalization group for the one-flavor lattice Gross–Neveu model with finite chemical potential
journal, April 2015

  • Takeda, Shinji; Yoshimura, Yusuke
  • Progress of Theoretical and Experimental Physics, Vol. 2015, Issue 4
  • DOI: 10.1093/ptep/ptv022

Controlling sign problems in spin models using tensor renormalization
journal, January 2014


Progress towards quantum simulating the classical O ( 2 ) model
journal, December 2014


Tensor renormalization group study of classical X Y model on the square lattice
journal, January 2014


Tensor Network Renormalization
journal, October 2015


Fine structure of the entanglement entropy in the O(2) model
journal, January 2016


Calculation of fermionic Green functions with Grassmann higher-order tensor renormalization group
journal, March 2018

  • Yoshimura, Yusuke; Kuramashi, Yoshinobu; Nakamura, Yoshifumi
  • Physical Review D, Vol. 97, Issue 5
  • DOI: 10.1103/PhysRevD.97.054511

Gauge-invariant rotor Hamiltonian from dual variables of 3D U ( 1 ) gauge theory
journal, April 2019


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

  • Kadoh, Daisuke; Kuramashi, Yoshinobu; Nakamura, Yoshifumi
  • Journal of High Energy Physics, Vol. 2018, Issue 3
  • DOI: 10.1007/JHEP03(2018)141

O(3) nonlinear sigma model in 1 + 1 dimensions with matrix product states
journal, April 2019


Coarse-graining renormalization by higher-order singular value decomposition
journal, July 2012


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


Gauge-invariant implementation of the Abelian-Higgs model on optical lattices
journal, October 2015


Faster methods for contracting infinite two-dimensional tensor networks
journal, December 2018


Impossibility of spontaneously breaking local symmetries
journal, December 1975


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


Classical direct interstring action
journal, April 1974


QCD as a quantum link model
journal, September 1999


Second Renormalization of Tensor-Network States
journal, October 2009


Tensor renormalization group algorithms with a projective truncation method
journal, April 2019


Worm Algorithms for Classical Statistical Models
journal, September 2001


Quantum link models: A discrete approach to gauge theories
journal, May 1997