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.^[3]

The material is modelled as a lattice with atoms in the sites with conduction electrons (or holes) moving between them, like in the Hubbard model. Unlike the Hubbard model, the electrons are strongly-correlated, meaning the electrons are sensitive to reciprocal coulombic repulsion, and so are less likely to occupy lattice sites already occupied by another electron. 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. In the t-J model, instead of U, there is the parameter J, function of the ratio t/U.

Like the Hubbard model, it is a prospective microscopic theory of high temperature superconductivity in cuprate superconductors which arise from doped antiferromagnets, particularly in the case where the lattice considered is the two-dimensional lattice.^[4][5] Cuprate superconductors are currently (as of 2024) the superconductors with the highest known superconducting transition temperature at ambient pressure, but there is no consensus on the microscopic theory responsible for their superconducting transition.