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

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 nearestneighbor attraction. BCS theory can then be applied with arbitrary analytical control, from which nodeless d-wave or s-wave superconductivity can result.1 arXiv:1906.06344v1 [cond-mat.str-el] 14 Jun 2019(1)] that we study. This model includes a nextnearest-neighbor hopping t across the dashed gray links instead of a nearest-neighbor hopping t across the solid black links. The model also includes an antiferromagnetic Ising interaction J z and nearest-neighbor repulsion V across each solid black link. Unlike a nearest-neighbor hopping t, the next-nearest-neighbor hopping t does not frustrate the antiferromagnetic interaction. The red and blue arrows denote spin up and spin down fermions.by (unphysical 1 ) phase separation [9]. To make progress, many works have considered a large variety of modifications to the t-J model in order to improve analytical tractability. Such modifications include explicit symmetry breaking [12,13], large spatial dimension [14], large N [15], nonlocality [16,17], SYK-like nonlocality with large N [18], and replacing the Heisenberg interaction J with an Ising interaction J z [19][20][21][22][23][24]. In this work, our goal will be to study the simplest modification to the t-J model (that does not enlarge the Hilbert space) such that a superconducting phases exists and can be well-understood with analytical control. Since the nearest-neighbor hopping frustrates the antiferromagnetic order in the t-J model, we replace the nearest-neighbor hopping t with a next-nearest-neighbor hopping t which does not compete with antiferromagnetism. To further simplify, we replace the Heisenberg interaction J with an antiferromagnetic Ising interaction J z . 2 We also add a nearest-neighbor repulsion V to prevent unphysical charge separation. See Fig. 1.The absence of a nearest-neighbor hopping may be an unrealistic aspect of our model. However, this omission is loosely motivated since nearest-neighbor hopping is strongly suppressed in t-J-like models near half-filling when J is large [27][28][29]. Also note that nextnearest-neighbor hopping keeps the fermions on the same sublattice, ...