T J model - Alchetron, The Free Social Encyclopedia

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,

n_i = ∑σâ†
iσâ
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 S_i and S_j, and the number operators n_i and n_j 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

(Text) CC BY-SA