Exact solution of the p+ip pairing Hamiltonian and a hierarchy of integrable models

TL;DR

This paper derives an exactly solvable p+ip pairing Hamiltonian with anyonic degrees of freedom, analyzes its ground-state phases, and reveals a rich topological phase diagram including the Moore-Read state.

Contribution

It introduces a new integrable pairing model with anyonic degrees of freedom and thoroughly analyzes its topological phases and ground-state properties.

Findings

The ground-state phase diagram has three distinct phases.

Identifies a boundary line with gapless excitations at zero chemical potential.

Finds the Moore-Read state on a specific phase boundary.

Abstract

Using the well-known trigonometric six-vertex solution of the Yang-Baxter equation we derive an integrable pairing Hamiltonian with anyonic degrees of freedom. The exact algebraic Bethe ansatz solution is obtained using standard techniques. From this model we obtain several limiting models, including the pairing Hamiltonian with p+ip-wave symmetry. An in-depth study of the p+ip model is then undertaken, including a mean-field analysis, analytic and numerical solution of the Bethe ansatz equations, and an investigation of the topological properties of the ground-state wavefunction. Our main result is that the ground-state phase diagram of the p+ip model consists of three phases. There is the known boundary line with gapless excitations that occurs for vanishing chemical potential, separating the topologically trivial strong pairing phase and the topologically non-trivial weak pairing phase. We argue that a second boundary line exists separating the weak pairing phase from a topologically trivial weak coupling BCS phase, which includes the Fermi sea in the limit of zero coupling. The ground state on this second boundary line is the Moore-Read state.