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 grand challenge. We have recently shown that this can be done the Hatsugai-Kohmoto (HK) which understood generally minimal breaks non-local $\mathbb Z_2$ symmetry of Fermi liquid, thereby constituting new quartic fixed point physics [Phillips et al., Nature Physics 16, 1175 (2020); Huang (2022)]. In current work, we compute thermodynamics, condensation energy, and electronic such NMR relaxation rate $1/T_1$ ultrasonic attenuation rate. Key differences arise with standard BCS analysis liquid: 1) free energy exhibits local minimum at $T_p$ where pairing gap turns on discontinuously above critical value repulsive HK interaction, indicating first-order transition, 2) tri-critical emerges, demarcating boundary between second-order transition novel regime, 3) Mottness changes sign coefficient in Landau-Ginzburg free-energy fuctional relative to BCS, 4) obtains strongly interacting it is underlies generic 5) exceeds theory suggesting multiple bands might way enhancing superconducting, 6) heat-capacity jump non-universal increases scale, 7) destroys Hebel-Slichter peak NMR, 8) enhances fall-off temperature $T_p$. As several these are observed cuprates, our here points forward computing correlated electron matter.