An exactly solvable BCS-Hubbard Model in arbitrary dimensions

TL;DR

This paper introduces an exactly solvable BCS-Hubbard model in arbitrary dimensions, revealing new insights into p-wave superconductivity with Hubbard interactions and generalizing Kitaev's exactly solvable models.

Contribution

The paper presents a novel exactly solvable BCS-Hubbard model for arbitrary dimensions, extending Kitaev's construction to interacting lattice fermions with equal spin pairing.

Findings

Model is exactly solvable when pairing amplitude equals hopping amplitude

Solution parallels Kitaev honeycomb model for spins

Framework generalizes to a large class of lattice fermion models

Abstract

We introduce in this paper an exact solvable BCS-Hubbard model in arbitrary dimensions. The model describes a p-wave BCS superconductor with equal spin pairing moving on a bipartite (cubic, square etc.) lattice with on site Hubbard interaction $U$. We show that the model becomes exactly solvable for arbitrary $U$ when the BCS pairing amplitude $\Delta$ equals the hopping amplitude $t$. The nature of the solution is described in detail in this paper. The construction of the exact solution is parallel to the exactly solvable Kitaev honeycomb model for $S=1/2$ quantum spins and can be viewed as a generalization of Kitaev's construction to $S=1/2$ interacting lattice fermions. The BCS-Hubbard model discussed in this paper is just an example of a large class of exactly solvable lattice fermion models that can be constructed similarly.