Hole dynamics in an antiferromagnet across a deconfined quantum critical point

We study the effects of a small density of holes, δ, on a square-lattice antiferromagnet undergoing a continuous transition from a Néel state to a valence bond solid at a deconfined quantum critical point. We argue that at nonzero δ, it is likely that the critical point broadens into a non-Fermi-liquid “holon-metal” phase with fractionalized excitations. The holon-metal phase is flanked on both sides by Fermi-liquid states with Fermi surfaces enclosing the usual Luttinger area. The electronic quasiparticles carry distinct quantum numbers in the two Fermi-liquid phases, and consequently we find that the ratio lim_δ→0A_F∕δ (where A_F is the area of a single hole pocket) has a factor of 2 discontinuity across the quantum critical point of the insulator. Note, however, that at δ>0, there is no direct transition between these two Fermi-liquid states with distinct Fermi surface configurations; instead, there is an intermediate holon-metal phase whose width shrinks to zero as δ→0. We demonstrate that the electronic spectrum at the δ→0 transition is described by the “boundary” critical theory of an impurity coupled to a (2+1)-dimensional conformal field theory. We compute the finite temperature quantum critical electronic spectra and show that they resemble “Fermi arc” spectra seen in recent photoemission experiments on the pseudogap phase of the cuprates.