An exactly solvable BCS-Hubbard Model in arbitrary dimensions

In this talk, we present 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 onsite 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. In this limit, the model is non-magnetized without interaction while it becomes an anti-ferromagnet for arbitrary small interaction. The solitonic excitation of this model shows a transition from spin 1/2 fermionic excitation to spin 1 bosonic excitation. 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 [1-2]. The BCS-Hubbard model discussed is just an example of a large class of exactly solvable lattice fermion models that can be constructed similarly. Our arxiv preprint is available at Ref.[3].

[1] Kitaev, A. (2006). Annals of Physics, 321(1), 2-111.
[2] Feng, X. Y., Zhang, G. M., & Xiang, T. (2007). Physical review letters, 98(8), 087204.
[3] Chen, Z., Li, X., & Ng, T. K. (2017). arXiv preprint arXiv:1709.08411.