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

Boye Buyens, Simone Montangero, Jutho Haegeman, Frank Verstraete, and Karel Van Acoleyen
Phys. Rev. D 95, 094509 – Published 24 May 2017

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 QED2, 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.

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  • Received 9 March 2017

DOI:https://doi.org/10.1103/PhysRevD.95.094509

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Boye Buyens1, Simone Montangero2,3, Jutho Haegeman1, Frank Verstraete1,4, and Karel Van Acoleyen1

  • 1Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium
  • 2Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technology (IQST), Ulm University, Albert-Einstein-Allee 11, D-89069 Ulm, Germany
  • 3Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
  • 4Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria

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Issue

Vol. 95, Iss. 9 — 1 May 2017

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