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

Kevin Slagle

doi:10.21468/scipostphys.7.4.046

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_zJz-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_zJz, 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.

Highlights

The t-J and Hubbard models have been studied extensively as toy models for high-temperature superconductivity in the cuprate superconductors [1,2,3,4]
Due to the secondnearest-neighbor hopping and antiferromagnetic ground state, the onsite Hubbard repulsion effectively disappears from the effective Hamiltonian HAF [Eq (6)], and the antiferromagnetic
Heisenburg term leads to an effective nearest-neighbor attractive interaction V0 in the antiferromagnetic ground state

Summary

Introduction

The t-J and Hubbard models have been studied extensively as toy models for high-temperature superconductivity in the cuprate superconductors [1,2,3,4]. The first term hops electrons diagonally between next-nearest-neighbor sites 〈〈i j〉〉 while imposing the ni ≤ 1 constraint via the projection operator P, which projects out ni = 2 states. We argue that the ground state never has parallel spins in the V0 |t | Jz limit for sufficiently large electron fillings. This occurs because all of the eigenstates have definite Sz spin on each sublattice, and the lowest energy state is a fully-polarized antiferromagnet where one sublattice has only spin-up electrons and the other has only spin-down. In Appendix A, we provide a rigorous numerical argument that the ground state is fully antiferromagnetic when V0 |t | where we bound nc < 0.265

Effective Model

Conclusion

A Saturated Antiferromagnetism

B Mean Field Theory

Approximate Gap Scaling