Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics

Nikolai Zerf, Rufus Boyack, Peter Marquard, John A. Gracey, and Joseph Maciejko
Phys. Rev. D 101, 094505 – Published 14 May 2020
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Abstract

Elucidating the phase diagram of lattice gauge theories with fermionic matter in 2+1 dimensions has become a problem of considerable interest in recent years, motivated by physical problems ranging from chiral symmetry breaking in high-energy physics to fractionalized phases of strongly correlated materials in condensed matter physics. For a sufficiently large number Nf of flavors of four-component Dirac fermions, recent sign-problem-free quantum Monte Carlo studies of lattice quantum electrodynamics (QED3) on the square lattice have found evidence for a continuous quantum phase transition between a power-law correlated conformal QED3 phase and a confining valence-bond-solid phase with spontaneously broken point-group symmetries. The critical continuum theory of this transition was shown to be the O(2) QED3-Gross-Neveu model, equivalent to the gauged Nambu–Jona-Lasinio model, and critical exponents were computed to first order in the large-Nf expansion and the ε expansion. We extend these studies by computing critical exponents to second order in the large-Nf expansion and to four-loop order in the ε expansion below four spacetime dimensions. In the latter context, we also explicitly demonstrate that the discrete Z4 symmetry of the valence-bond-solid order parameter is dynamically enlarged to a continuous O(2) symmetry at criticality for all values of Nf.

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  • Received 31 March 2020
  • Accepted 28 April 2020

DOI:https://doi.org/10.1103/PhysRevD.101.094505

© 2020 American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Nikolai Zerf1, Rufus Boyack2,3, Peter Marquard4, John A. Gracey5, and Joseph Maciejko2,3

  • 1Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany
  • 2Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
  • 3Theoretical Physics Institute, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
  • 4Deutsches Elektronen Synchrotron (DESY), Platanenallee 6, D-15738 Zeuthen, Germany
  • 5Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, P.O. Box 147, Liverpool, L69 3BX, United Kingdom

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Issue

Vol. 101, Iss. 9 — 1 May 2020

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