Solvable two-dimensional superconductors with l-wave pairing

Luca Lepori; Marco Roncaglia

doi:10.1103/PhysRevB.98.144504

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Solvable two-dimensional superconductors with l-wave pairing

Luca Lepori, Marco Roncaglia

DOI 10.1103/PhysRevB.98.144504 · Physical Review B

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Abstract

We analyze a family of two-dimensional BCS Hamiltonians with general l-wave pairing interactions, classifying the models in this family that are Bethe-ansatz solvable in the finite-size regime. We show that these solutions are characterized by nontrivial winding numbers, associated with topological phases, in some part of the corresponding phase diagrams. By means of a comparative study, we demonstrate benefits and limitations of the mean-field approximation, which is the standard approach in the limit of a large number of particles. The mean-field analysis also allows us to extend part of the results beyond integrability, clarifying the peculiarities associable with the integrability itself.