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The t-J model is believed to be a minimal model that may be capable ofdescribing the low-energy physics of the cuprate superconductors. However,although the t-J model is simple in appearance, obtaining a detailedunderstanding of its phase diagram has proved to be challenging. We aretherefore motivated to study modifications to the t-J model such that its phasediagram and mechanism for d-wave superconductivity can be understoodanalytically without making uncontrolled approximations. The modified model weconsider is a $t'$-$J_z$-$V$ model on a square lattice, which has asecond-nearest-neighbor hopping $t'$ (instead of a nearest-neighbor hopping$t$), an Ising (instead of Heisenberg) antiferromagnetic coupling $J_z$, and anearest-neighbor repulsion $V$. In a certain strongly interacting limit, theground state is an antiferromagnetic superconductor that can be describedexactly by a Hamiltonian where the only interaction is a nearest-neighborattraction. BCS theory can then be applied with arbitrary analytical control,from which nodeless d-wave or s-wave superconductivity can result.

Unfrustrating the t-J Model: d-wave BCS Superconductivity in the $t'$-$J_z$-$V$ Model