Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical properties of the valence-bond-solid transition in lattice
  quantum electrodynamics   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 $N_f$.

34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn