Intertwined superconductivity, charge-density wave, and supersolid order in topologically trivial flat-bands

Superconductivity in the limit of a vanishing bandwidth in isolated bands is a classic example of a non-perturbative problem, where BCS theory does not apply. What sets the superconducting phase stiffness, and relatedly the transition temperature, in the flat-band limit is a question of both fundamental and practical interest. We will demonstrate using analytical and numerically exact quantum Monte-Carlo computations that the phase stiffness is set by the strength of attractive interactions even for models with topologically trivial flat-bands, as long as certain criteria are met. By including further neighbor interactions, we can drive the system into a panoply of ordered or phase-separated states.