T-J model


The t-J model was first derived in 1977 from the Hubbard model by Józef Spałek. The model describes strongly-correlated electron systems. It is used to calculate high temperature superconductivity states in doped antiferromagnets.
The t-J Hamiltonian is:
where
The Hamiltonian of the t1-t2-J model in terms of the CP1 generalized model
is:
where the fermionic operators c and c, the spin operators Si and Sj, and the number operators ni and nj all act on restricted Hilbert space and the doubly-occupied states are excluded. The sums in the above-mentioned equation are over all sites of a 2-dimensional square lattice, where ⟨…⟩ and ⟨⟨…⟩⟩ denote the nearest and next-nearest neighbors, respectively.