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Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks

Boye Buyens, Simone Montangero, Jutho Haegeman UGent, Frank Verstraete UGent and Karel Van Acoleyen UGent (2017) PHYSICAL REVIEW D. 95(9).
abstract
It has been established that matrix product states can be used to compute the ground state and single-particle excitations and their properties of lattice gauge theories at the continuum limit. However, by construction, in this formalism the Hilbert space of the gauge fields is truncated to a finite number of irreducible representations of the gauge group. We investigate quantitatively the influence of the truncation of the infinite number of representations in the Schwinger model, one-flavor QED 2, with a uniform electric background field. We compute the two-site reduced density matrix of the ground state and the weight of each of the representations. We find that this weight decays exponentially with the quadratic Casimir invariant of the representation which justifies the approach of truncating the Hilbert space of the gauge fields. Finally, we compute the single-particle spectrum of the model as a function of the electric background field.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
MASSIVE SCHWINGER MODEL, DENSITY-MATRIX RENORMALIZATION, ENTANGLED PAIR STATES, QUARK CONFINEMENT, HAMILTONIAN-FORMULATION, PRODUCT STATES, LIQUID-HELIUM, CHARGE, TEMPERATURE, FIELD
journal title
PHYSICAL REVIEW D
Phys. Rev. D
volume
95
issue
9
article number
094509
pages
23 pages
Web of Science type
Article
Web of Science id
000402009000002
ISSN
2470-0010
DOI
10.1103/PhysRevD.95.094509
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
8521403
handle
http://hdl.handle.net/1854/LU-8521403
date created
2017-05-27 05:16:58
date last changed
2017-10-11 08:59:00
@article{8521403,
  abstract     = {It has been established that matrix product states can be used to compute the ground state and single-particle excitations and their properties of lattice gauge theories at the continuum limit. However, by construction, in this formalism the Hilbert space of the gauge fields is truncated to a finite number of irreducible representations of the gauge group. We investigate quantitatively the influence of the truncation of the infinite number of representations in the Schwinger model, one-flavor QED 2, with a uniform electric background field. We compute the two-site reduced density matrix of the ground state and the weight of each of the representations. We find that this weight decays exponentially with the quadratic Casimir invariant of the representation which justifies the approach of truncating the Hilbert space of the gauge fields. Finally, we compute the single-particle spectrum of the model as a function of the electric background field.},
  articleno    = {094509},
  author       = {Buyens, Boye and Montangero, Simone and Haegeman, Jutho and Verstraete, Frank and Van Acoleyen, Karel},
  issn         = {2470-0010},
  journal      = {PHYSICAL REVIEW D},
  keyword      = {MASSIVE SCHWINGER MODEL,DENSITY-MATRIX RENORMALIZATION,ENTANGLED PAIR STATES,QUARK CONFINEMENT,HAMILTONIAN-FORMULATION,PRODUCT STATES,LIQUID-HELIUM,CHARGE,TEMPERATURE,FIELD},
  language     = {eng},
  number       = {9},
  pages        = {23},
  title        = {Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks},
  url          = {http://dx.doi.org/10.1103/PhysRevD.95.094509},
  volume       = {95},
  year         = {2017},
}

Chicago
Buyens, Boye, Simone Montangero, Jutho Haegeman, Frank Verstraete, and Karel Van Acoleyen. 2017. “Finite-representation Approximation of Lattice Gauge Theories at the Continuum Limit with Tensor Networks.” Physical Review D 95 (9).
APA
Buyens, B., Montangero, S., Haegeman, J., Verstraete, F., & Van Acoleyen, K. (2017). Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks. PHYSICAL REVIEW D, 95(9).
Vancouver
1.
Buyens B, Montangero S, Haegeman J, Verstraete F, Van Acoleyen K. Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks. PHYSICAL REVIEW D. 2017;95(9).
MLA
Buyens, Boye, Simone Montangero, Jutho Haegeman, et al. “Finite-representation Approximation of Lattice Gauge Theories at the Continuum Limit with Tensor Networks.” PHYSICAL REVIEW D 95.9 (2017): n. pag. Print.