= t-J model
{c}
{title2=$J=4t^2/U$}
An effective low-energy lattice model obtained from a strongly repulsive <Hubbard model> near one <electron> per site. The retained Hilbert space excludes double occupancy. Its usual nearest-neighbor Hamiltonian has projected hopping $-t\sum_{\langle ij\rangle,\sigma}(\widetilde c_{i\sigma}^\dagger\widetilde c_{j\sigma}+\mathrm{h.c.})$ and antiferromagnetic <superexchange> $J\sum_{\langle ij\rangle}(\mathbf S_i\cdot\mathbf S_j-n_in_j/4)$. Virtual intermediate states with one double occupancy cost <energy> $U$, giving $J=4t^2/U$ to leading order. Three-site hopping terms of the same expansion order are omitted in this simplified version.
At half filling the projected hopping is blocked. Doped holes restore charge motion coupled to spin correlations. Nearest-neighbor singlet pairing can support a <d-wave bond order> ansatz on a square lattice, but the Hamiltonian alone is not a proof of a unique superconducting <ground state> for all parameters.
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