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:


  • ij is the sum over nearest-neighbor sites i and j,
  • â
    , â
    are the fermionic creation and annihilation operators,
  • σ is the spin polarization,
  • t is the hopping integral,
  • J is the coupling constant, J = 4t2/U,
  • U is the coulombic repulsion,
  • ni = σâ
    is the particle number at site i, and
  • Si, Sj are the spins on sites i and j.

Connection to the high-temperature superconductivity[edit]

The Hamiltonian of the t1-t2-J model in terms of the CP1 generalized model is:[1]

where the fermionic operators c
and c
, the spin operators Si and Sj, and the number operators ni and nj all act on restricted Hilbert space and the doubly-occupied states are excluded. The sums in the above-mentioned equation are over all sites of a 2-dimensional square lattice, where ⟨…⟩ and ⟨⟨…⟩⟩ denote the nearest and next-nearest neighbors, respectively.


  1. ^ Karchev, Naoum (1998). "Generalized CP1 model from the t1-t2-J model". Phys. Rev. B. 57: 10913. doi:10.1103/PhysRevB.57.10913. 
  • Fazekas, Patrik, Lectures on Correlation and Magnetism, p. 199 [full citation needed]
  • Spałek, Józef (2007). "t-J model then and now: A personal perspective from the pioneering times". Acta Phys. Polon. A. 111: 409–424. arXiv:0706.4236Freely accessible.