Deconfined Critical Point in a Doped Random Quantum Heisenberg Magnet

We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interaction between any pair of sites and a constraint of no double occupancy. A perturbative renormalization group analysis yields a critical point with fractionalized excitations at a nonzero critical value p c of the hole doping p away from the half-filled insulator. We compute the renormalization group to two loops, but some exponents are obtained to all loop order. We argue that the critical point p c is flanked by confining phases: a disordered Fermi liquid with carrier density 1 p for p > p c and a metallic spin glass with carrier density p for p < p c . Additional evidence for the critical behavior is obtained from a large-M analysis of a model which extends the SU(2) spin symmetry to SUM. We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.