Spinless Fermions on a Checkerboard Lattice

We present a study of the low-energy physics of a spinless fermionic model on a checkerboard lattice at half-filling. The bosonic version of this model has been recently studied and found to have several unusual features. Fermionic models tend to be more interesting: the inherent sign problem resulting from the fermionic statistics makes them notoriously difficult to handle. The low-energy physics of the model can be described by a fermionic quantum loop model on the square lattice. We found a non-local transformation that can, in certain cases, cure the sign problem. We also identified a large class of fluctuationless states specific to the fermionic models -- a result hinting at a possible explanation of the extended ground-state entropy recently found in a few other fermionic models. Finally, we looked at the so-called Rokhsar-Kivelson quantum critical point, where we found the exact ground state(s) as well as studied the low-lying excitations. This allowed us to make several educated guesses about the phase diagram for the model in question. [1] F.~Pollmann, J.~J.~Betouras, K.~Shtengel, and P.~Fulde, Phys. Rev. Lett. \textbf{97}, 170407 (2006)