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

Zerf, Nikolai, Boyack, Rufus, Marquard, Peter, Gracey, John A ORCID: 0000-0002-9101-2853 and Maciejko, Joseph
(2020) Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics. PHYSICAL REVIEW D, 101 (9). 094505-.

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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 $N_f$ of flavors of four-component Dirac fermions, recent sign-problem-free quantum Monte Carlo studies of lattice quantum electrodynamics (QED$_3$) on the square lattice have found evidence for a continuous quantum phase transition between a power-law correlated conformal QED$_3$ 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 $O(2)$ QED$_3$-Gross-Neveu model, equivalent to the gauged Nambu-Jona-Lasinio model, and critical exponents were computed to first order in the large-$N_f$ expansion and the $\epsilon$ expansion. We extend these studies by computing critical exponents to second order in the large-$N_f$ expansion and to four-loop order in the $\epsilon$ expansion below four spacetime dimensions. In the latter context, we also explicitly demonstrate that the discrete $\mathbb{Z}_4$ symmetry of the valence-bond-solid order parameter is dynamically enlarged to a continuous $O(2)$ symmetry at criticality for all values of $N_f$.

Item Type: Article
Additional Information: 16 pages, 6 figures, 8 tables; v2: published version
Uncontrolled Keywords: cond-mat.str-el, cond-mat.str-el, hep-lat, hep-th
Depositing User: Symplectic Admin
Date Deposited: 30 Apr 2020 10:38
Last Modified: 18 Jan 2023 23:53
DOI: 10.1103/PhysRevD.101.094505
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