Charge degrees of freedom in the quarter-filled checkerboard lattice

For a systematic study of charge degrees of freedom in lattices with geometric frustration, we consider spinless fermions on the checkerboard lattice with nearest-neighbor hopping t and nearest-neighbor repulsion V at quarter-filling. An effective Hamiltonian in the limit vertical bar t vertical bar << V is given to lowest non-vanishing order by the ring exchange (similar to t(3)/V-2). We show that the system can equivalently be described by hard-core bosons and map the model to a confining U(l) lattice gauge theory. (c) 2006 Elsevier B.V. All rights reserved.