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

Author
Organization
Project
QUTE (Quantum Tensor Networks and Entanglement)
Project
ERQUAF (Entanglement and Renormalisation for Quantum Fields)
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.
Keywords
MASSIVE SCHWINGER MODEL, DENSITY-MATRIX RENORMALIZATION, ENTANGLED PAIR STATES, QUARK CONFINEMENT, HAMILTONIAN-FORMULATION, PRODUCT STATES, LIQUID-HELIUM, CHARGE, TEMPERATURE, FIELD

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Citation

Please use this url to cite or link to this publication:

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.
@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},
}

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