Pseudospin representation of the two-dimensional t-J model

We investigate the two-dimensional t-J model describing most of the physical properties of the copper-oxide materials. In this model, due to the single occupancy constraint, the electron operators no longer obey the fermionic anti-commutation relations. By introducing pseudospins associated with empty sites, we derive a representation of the t-J model that consists of spinless fermions and local spins. Within a mean-field approximation, we show that our representation of the t-J model corresponds to the antiferromagnetic Heisenberg model in an effective magnetic field induced by hole doping δ. We show that the staggered magnetization decreases with increasing hole doping δ and disappears at reasonable value of the critical doping δ_c, which is in good agreement with experiments and numerical calculations.