t-J model

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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:


  • - sum over nearest-neighbor sites i and j,
  • - fermionic creation and annihilation operators,
  • - spin polarization,
  • - hopping integral
  • - coupling constant ,
  • - coulomb repulsion,
  • - particle number at the site i, and
  • - spins on the sites i and j.

Connection to the high-temperature superconductivity[edit]

The Hamiltonian of the model in terms of generalized model reads [1]

where fermionic operators , , the spin operators and , number operators and act on restricted Hilbert space and the doubly-occupied states are excluded. The sums in above mentioned equation are over all sites of a (2-d) square lattice, where and denote nearest and next-to-the-nearest neighbors, respectively.


  • Lectures on Correlation and Magnetism, [Patrik Fazekas],[page no. :199]
  • t-J model then and now: A personal perspective from the pioneering times, Józef Spałek, arXiv:0706.4236