Solvable 2D superconductors with l-wave pairing

TL;DR

This paper classifies and analyzes 2D BCS Hamiltonians with l-wave pairing, identifying topological phases and evaluating the mean-field approximation's effectiveness and limitations.

Contribution

It provides a classification of Bethe-ansatz solvable models with topological phases and compares exact solutions with mean-field results.

Findings

Identifies solvable models with nontrivial topological winding numbers

Highlights the strengths and limitations of the mean-field approximation

Extends some results beyond integrability using mean-field analysis

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 to extend part of the results beyond integrability, clarifying the peculiarities associable with the integrability itself.