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# Model t-J

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:

$\hat H = -t\sum_{ij\sigma}\hat a^\dagger_{i\sigma} \hat a_{j\sigma} + J\sum_{}\vec S_{i}\cdot \vec S_{j}$

$\hat a^\dagger_{i\sigma} , \hat a_{j\sigma}$ - annihilation and creation operators

σ - spin polarization

J - coupling constant J = 4t2 / U

U - coulomb repulsion

$\vec S_i, \vec S_j$ - spins on i and j node