t-J model

In solid-state physics, the t-J model is a model first derived by Józef Spałek[1] to explain antiferromagnetic properties of Mott insulators,[2] taking into account experimental results about the strength of electron-electron repulsion in these materials.

In the basic Hubbard model, the repulsion, indicated by U, can be small or even zero, and electrons are more free to jump (hopping, parametrized by t as transfer or tunnel) from one site to another.

of the Hubbard model using the Schrieffer–Wolff transformation, with the transformation generator depending on t/U and excluding the possibility for electrons to doubly occupy a lattice's site,[6] which results in:[7] where the term in t corresponds to the kinetic energy and is equal to the one in the Hubbard model.

[1] The parameters are: If ni = 1, that is when in the ground state, there is just one electron per lattice's site (half-filling), the model reduces to the Heisenberg model and the ground state reproduce a dielectric antiferromagnets (Mott insulator).

[8] The model can be further extended considering also the next-nearest-neighbor sites and the chemical potential to set the ground state in function of the total number of particles:[9][10] where ⟨...⟩ and ⟨⟨...⟩⟩ denote the nearest and next-nearest neighbors, respectively, with two different values for the hopping integral (t1 and t2) and μ is the chemical potential.