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 SU(M). We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.