## SciPost Submission Page

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

### by Kevin Slagle

### Submission summary

As Contributors: | Kevin Slagle |

Arxiv Link: | https://arxiv.org/abs/1906.06344v1 |

Date submitted: | 2019-08-03 |

Submitted by: | Slagle, Kevin |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | Condensed Matter Physics - Theory |

### Abstract

The t-J model is believed to be a minimal model that may be capable of describing the low-energy physics of the cuprate superconductors. However, although the t-J model is simple in appearance, obtaining a detailed understanding of its phase diagram has proved to be challenging. We are therefore motivated to study modifications to the t-J model such that its phase diagram and mechanism for d-wave superconductivity can be understood analytically without making uncontrolled approximations. The modified model we consider is a t'-J_z-V model on a square lattice, which has a second-nearest-neighbor hopping t' (instead of a nearest-neighbor hopping t), an Ising (instead of Heisenberg) antiferromagnetic coupling J_z, and a nearest-neighbor repulsion V. In a certain strongly interacting limit, the ground state is an antiferromagnetic superconductor that can be described exactly by a Hamiltonian where the only interaction is a nearest-neighbor attraction. BCS theory can then be applied with arbitrary analytical control, from which nodeless d-wave or s-wave superconductivity can result.