Cooling fermi gases through entropy redistribution in flat band systems

Recent experimental breakthroughs have established entropy redistribution as a viable way to achieve low entropy quantum gases, which is a prerequisite for observing quantum manybody phases of interest. These cooling schemes typically cool a low entropy gapped phase, such as a band insulator, with a high entropy capacity phase as the entropy reservoir, such as a metallic state. The entropic state is then separated from the system of interest. In this work, we numerically investigate the possibility of using a lattice structure with a macroscopic degeneracy in the band structure, commonly known as a flat band, as the entropy reservoir. We first obtain the equation of states of interacting fermions on a sawtooth lattice numerically using tensor network methods, and evaluate the reduction in entropy in the system, assuming that the system of interest thermalizes with the reservoir. We then perform time-dependent Hartree-Fock calculations to assess the experimental feasibility of the cooling scheme.