Thermodynamics and coherence effects in the Hatsugai-Kohmoto superconductor

Soluble Hamiltonian models with unconventional superconductivity are few and far between. The Hatsugai-Kohmoto superconductor is one such model. In a previous work, we have shown that it exhibits a number of striking phenoma, including (1) a gap-to-T_c ratio that diverges in the weak pair coupling limit; (2) a shift in spectral weight across the superconducting transition, (in a certain regime) on the order of the colour change seen in BSCCO; and (3) novel elementary excitations that descend from its non-Fermi liquid normal state. We further clarify the nature of this superconductor from the perspective of its thermodynamics and some foundational experimental observables. Specifically, we consider its thermodynamic entropy, specific heat, and free energy, as well as the system's ultrasonic attenuation and nuclear spin relaxation rates.