Fractional fermionic Mott insulator and high-temperature superconductor in the doublon-conserving Hubbard model

The Hubbard model's doublon-conserving (DC) series expansion most directly mimics the true Hamiltonian dynamic (which does not conserve doublon number) when interaction dominates over bandwidth and the series can be truncated at low order in t/u. This work explores low-temperature electronic and superconducting orders driven by a renormalized particle-hole symmetric DC Hubbard model at intermediate coupling crucially including correlated hopping, accompanied by strong, exotic three-body fluctuations at finite temperature. Fluctuations couple not only to spins and charges, but to their hoppings and currents, and include terms promoting chirality. Hartree-Fock calculations reveal a spontaneous metric fostering exoticism including unstable gauged ferromagnetism with undamped Higgs mode at half-filling, antiferromagnetism, a strongly insulating Wigner crystal of holons at fractional filling, and gapless striped states. BdG theory incorporates Hirsch's s-wave superconductor, but reveals a tendency to inhomogeneity and stripey-intertwining with charge and spin order. The harmony of Hubbard U, correlated hopping, and superexchange strongly prefers d-wave pairing over s-wave. Including the DC current in a linear response calculation reveals distinctly non-BCS electrodynamics, including a vanishing of superfluid density approaching half-filling. The pivotal role of t' is explored alongside psuedogap candidate-states.