Strongly correlated electrons: the t—J model

A systematic study is made of the t—J model as a working model for copper oxide high-T_c superconductors. The main focus is on the near-half- filling region (low hole concentrations) relevant to these materials. The theory of the magnetic polaron, which is a charge carrier traveling in an antiferromagnetic matrix, and the theory of antiferromagnetic ordering are discussed in a unified framework. The spin liquid state beyond the antiferromagnetic phase is examined. The Hamiltonian parameters — hole concentration phase diagram for the model is described and compared with that for the Hubbard model in the strong correlation limit. Two extensions of the t—J model, the t—t'—J model and the three-center interaction model, are discussed. Mostly analityc strong correlation techniques are employed in this review.