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A comprehensive understanding of the physics of the Mott insulator has proved elusive due to the absence of any small parameter in the problem. We present a zero-temperature renormalisation group analysis of the one-band Hubbard model in two dimensions at, and away from, half-filling. We find that the transition in the half-filled system involves, for any Hubbard repulsion, passage from a non-Fermi liquid metallic state to a topologically-ordered gapped Mott liquid through a pseudogapped phase. The pseudogap is bookended by Fermi surface topology-changing Lifshitz transitions: one involving a disconnection at the antinodes, the other a final gapping at the nodes. Upon doping, we demonstrate the collapse of the Mott state at a quantum critical point possessing a nodal non-Fermi liquid with superconducting fluctuations, and spin-gapping away from the nodes. d-wave Superconducting order is shown to arise from this critical state of matter. Our findings are in striking agreement with results obtained in the cuprates, settling a long-standing debate on the origin of superconductivity in strongly correlated quantum matter.

Scaling theory for Mott–Hubbard transitions: I. T = 0 phase diagram of the 1/2-filled Hubbard model