Scaling theory for Mott-Hubbard transitions

We present a zero temperature nonperturbative analytical renormalization group (RG) investigation of the electronic Hubbard model in two dimensions on a square lattice. The source of quantum fluctuations in the occupation number of an electronic state is driven by elements of the Hubbard Hamiltonian that are off-diagonal in the Fock representation. Our RG resolves these quantum fluctuations via an iterative scheme involving the unitarily decoupling of an electronic state at every RG step. Stable fixed points of the RG identify effective Hamiltonians associated with various phases as a function of the fluctuation energy scale and doping. We find that the half-filled Mott transition involves passage from a gapless non-Fermi liquid to a gapped Mott liquid through a pseudogapped phase upon lowering the fluctuation scale. Upon doping, we show the collapse of the Mott liquid at a quantum critical point possessing d-wave structure in k-space: a nodal non-Fermi liquid with large superconducting fluctuations, and pre-formed Cooper pairs lying within spin-pseudogapped parts of k-space located away from the nodes. By allowing for symmetry breaking, we find an emergent d-wave superconducting phase surrounding the quantum critical point. This work is available at arXiv:1802.06528.