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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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 $N_f$ 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 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3085259 |
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