Charge degrees of freedom in frustrated lattices

We explore systematically the charge degrees of freedom in frustrated lattices. A model of spinless fermions on a checkerboard lattice with nearest-neighbor hopping t and Coulomb repulsion V is used at half and quarter fillings. Quantum fluctuations reduce the classical macroscopic degeneracy. For the strongly correlated limit V >> t, an added electron decays into two quasiparticles with fractional charge. We study the classical correlations and, by means of quantum field theory as well as axact diagonalisation, we also investigate the possibility of a confined or deconfined phase as well as the statistics of these quasiparticles.