Harman Patil (Editor)

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:

H ^ = t i j σ ( a ^ i σ a ^ j σ + a ^ j σ a ^ i σ ) + J i j ( S i S j n i n j 4 )


  • 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

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

    H = t 1 i , j ( c i σ c j σ + h . c . )   +   t 2 i , j ( c i σ c j σ + h . c . )   +   J i , j ( S i S j n i n j 4 )   μ i n i ,

    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.


    T-J model Wikipedia

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