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arXiv · 1407.3793

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

Gerardo Ortiz·Jorge Dukelsky·Emilio Cobanera·Carlos Esebbag·Carlo Beenakker
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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.

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Gerardo Ortiz, Jorge Dukelsky, Emilio Cobanera, Carlos Esebbag, Carlo Beenakker. 2014-07-14. Many-body characterization of topological superconductivity: The Richardson-Gaudin-Kitaev chain. https://doi.org/10.1103/physrevlett.113.267002

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