Correlated fermions on a checkerboard lattice

A model of strongly correlated spinless fermions on a checkerboard lattice is mapped onto a quantum fully packed loop model. We identify a large number of fluctuationless states specific to the fermionic case. We also show that for a class of fluctuating states the fermionic sign problem can be gauged away. This claim is supported by numerical evaluation of the low-lying states. Furthermore, we analyze excitations at the Rokhsar-Kivelson point of this model using the relation to the height model and the single-mode approximation.