Solvable model with interaction of pair dipoles in one dimension

Heinz–Jürgen Schmidt, Jerzy Gustaw Bartke

J. Dukelsky

J. Dukelsky, Carlos Esebbag, Peter Schuck

We present three classes of exactly solvable models for fermion and boson systems, based on the pairing interaction. These models are solvable in any dimension. As an example we show the first results for fermions interacting with repulsive pairing forces in a two-dimensional square lattice. In spite of the repulsive pairing force the exact results show attractive pair correlations.

Zewei Chen, Xiaohui Li, Tai Kai Ng

We introduce in this Letter 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 Δ equals the hopping amplitude t. The nature of the solution is described in detail in this Letter. 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 Letter is just an example of a large class of exactly solvable lattice fermion models that can be constructed similarly.

Nathan L. Harshman

Qiang Han, Jia Liu, Z. D. Wang

We solve exactly a BCS-type model of Dirac fermions in three dimension (3D) and show that 3D s-wave superconductors with spin-orbit interactions are equivalent to chiral p + ip-wave ones. In the presence of a Zeeman field, it is found that the reduced BCS Hamiltonian is also exactly solvable. Most intriguingly, a new type of FFLO ground state is rigorously revealed, in which the center-of-mass momentum of the fermion pair is proportional to the Zeeman field.