Spectral functions and optical conductivity of spinless fermions on a checkerboard lattice

We study the dynamical properties of spinless fermions on the checkerboard lattice. Our main interest is the limit of large nearest-neighbor repulsion V as compared with hopping parallel to t parallel to. The spectral functions show broad low-energy excitations which are due to the dynamics of fractionally charged excitations. Furthermore, it is shown that the fractional charges contribute to the electrical current density.