  Inspired by recent conflicting views on the order of the phase transition
from an antiferromagnetic Neel state to a valence bond solid, we use the
functional renormalization group to study the underlying quantum critical field
theory which couples two complex matter fields to a non-compact gauge field. In
our functional renormalization group approach we only expand in covariant
derivatives of the fields and use a truncation in which the full field
dependence of all wave-function renormalization functions is kept. While we do
find critical exponents which agree well with some quantum Monte Carlo studies
and support the scenario of deconfined criticality, we also obtain an
irrelevant eigenvalue of small magnitude, leading to strong corrections to
scaling and slow convergence in related numerical studies.
