Thermodynamics of an exactly solvable model for superconductivity in a doped Mott insulator

Computing superconducting properties starting from an exactly solvable model for a doped Mott insulator stands as a grand challenge. We have recently shown that this can be done starting from the Hatsugai-Kohmoto (HK) model, which can be understood generally as the minimal model that breaks the nonlocal Z2 symmetry of a Fermi liquid, thereby constituting a new quartic fixed point for Mott physics [Phillips et al., Nat. Phys. 16, 1175 (2020)1745-247310.1038/s41567-020-0988-4; Huang et al., Nat. Phys. (2022)]. In the current paper, we compute the thermodynamics, condensation energy, and electronic properties such as the NMR relaxation rate 1/T1 and ultrasonic attenuation rate. Key differences arise with the standard BCS analysis from a Fermi liquid: (1) the free energy exhibits a local minimum at Tp where the pairing gap turns on discontinuously above a critical value of the repulsive HK interaction, thereby indicating a first-order transition; (2) a tricritical point emerges, thereby demarcating the boundary between the standard second-order superconducting transition and the novel first-order regime; (3) Mottness changes the sign of the quartic coefficient in the Landau-Ginzburg free-energy functional relative to that in BCS; (4) as this obtains in the strongly interacting regime, it is Mott physics that underlies the generic first-order transition; (5) the condensation energy exceeds that in BCS theory suggesting that multiple Mott bands might be a way of enhancing superconducting; (6) the heat-capacity jump is nonuniversal and increases with the Mott scale; (7) Mottness destroys the Hebel-Slichter peak in NMR; and (8) Mottness enhances the fall-off of the ultrasonic attenuation at the pairing temperature Tp. As several of these properties are observed in the cuprates, our analysis here points a way forward in computing superconducting properties of strongly correlated electron matter.