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:

$hat\; H\; =\; -tsum\_\{ijsigma\}hat\; a^dagger\_\{isigma\}\; hat\; a\_\{jsigma\}+Jsum\_\{\}(vec\; S\_\{i\}cdot\; vec\; S\_\{j\}-n\_in\_j/4)$

$hat\; a^dagger\_\{isigma\}\; ,\; hat\; a\_\{jsigma\}$ - creation and annihilation operators

$sigma$ - spin polarization

$J$ - coupling constant $J\; =\; 4t^2/U$

$U$ - coulomb repulsion

$vec\; S\_i,\; vec\; S\_j$ - spins on i and j node