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:
- is the sum over nearest-neighbor sites i and j,
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 is the coulombic repulsion,
- ni = 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:
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.
- 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: .
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