Many-body characterization of topological superconductivity: The Richardson-Gaudin-Kitaev chain

TL;DR

This paper introduces an exactly solvable, number-conserving many-body model called the Richardson-Gaudin-Kitaev chain, which characterizes topological superconductivity through fermionic parity switches and a new topological invariant.

Contribution

It develops a novel integrable, interacting variation of the Kitaev model that remains exactly solvable and identifies topological features in many-body systems with conserved particle number.

Findings

Fermionic parity switches distinguish topological from trivial phases.

The model exhibits a third-order phase transition.

A closed-form topological invariant is derived.

Abstract

What distinguishes trivial from topological superluids in interacting many-body systems where the number of particles is conserved? Building on a class of integrable pairing Hamiltonians, we present a number-conserving, interacting variation of the Kitaev model, the Richardson-Gaudin-Kitaev chain, that remains exactly solvable for periodic and antiperiodic boundary conditions. Our model allows us to identify fermionic parity switches that distinctively characterize topological superconductivity in interacting many-body systems. Although the Majorana zero-modes in this model have only a power-law confinement, we may still define many-body Majorana operators by tuning the flux to a fermion parity switch. We derive a closed-form expression for an interacting topological invariant and show that the transition away from the topological phase is of third order.