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 $|t|$. The spectral functions show broad low-energy excitation which are due to the dynamics of fractionally charged excitations. Furthermore, it is shown that the fractional charges contribute to the electrical current density. 
F. Pollmann, P. Fulde, and E. Runge