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

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.

5 pages, 2 figures

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Cited by in corpus (9)

• A generalization of Bloch's theorem for arbitrary boundary conditions: Theory
• Exact solution to an interacting dimerized Kitaev model at symmetric point
• Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions
• Squaring the fermion: The threefold way and the fate of zero modes
• A variational method for integrability-breaking Richardson-Gaudin models
• Quantum phases of a one-dimensional Majorana-Bose-Hubbard model
• Two-fluid coexistence and phase separation in a one dimensional model with pair hopping and density interactions
• Polynomial description of inhomogeneous topological superconducting wires
• Many-body Majorana-like zero modes without gauge symmetry breaking