Abstract
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 | t | ⪡ V is given to lowest non-vanishing order by the ring exchange ( ∼ 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 ( 1 ) lattice gauge theory.
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