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 )

where

  • ∑⟨ij⟩ is the sum over nearest-neighbor sites i and j,
  • â†
    iσ    , â
    iσ     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†
    iσ    â
    iσ     is the particle number at site i, and
  • S→i, S→j 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†
    iσ     and c
    iσ    , 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.

    References

    T-J model Wikipedia
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