Duality between the SU(2) lattice gauge model and bosonic t − J model

Abstract We investigate the duality between the S U ( 2 ) lattice gauge model and the bosonic t − J model. We construct the relations between the gauge field operators and particle operators, and map the low-energy regime of the S U ( 2 ) lattice gauge model to a U ( 1 ) bosonic t − J model coupled with a U ( 1 ) gauge field. The mapped model can be interpreted as a bosonic t − J model with particle-hole symmetry, or a mean-field form of the bosonic t − J model with the coexistence of a two-particle pairing and four particle-pairing. The duality between the lattice gauge model and the bosonic t − J model provides a direct connection between gauge theory and strongly correlated systems.