Critical Anomalous Metal Near Superconductivity in a Random Hubbard Model

We study the quantum phase transition between a superconductor and a metal within a half-filled Hubbard model of electrons with random and all-to-all hopping and exchange. A perturbative renormalization group analysis yields a deconfined critical point at U=0 with fractionalized excitations. We obtain exponents for the electron and spin correlators to all orders in perturbation theory. These are same as those found in a random t-J model at finite doping [1] and exhibit a SYK-like behavior. We also calculate the exponents for the superconductor order parameter and density to one-loop order. A large M analysis for models with SU(M) spin symmetry provides additional evidence for the critical behavior. Investigation of the background conductivity at zero temperature indicates the existence of critical anomalous metal phase near superconductivity in this model.

[1] D. Joshi, C. Li, G. Tarnopolsky, A. Georges and S. Sachdev, Phys. Rev. X 10, 021033 (2020)