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Regensburg 2019 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 68: Topology: Other Topics

TT 68.3: Vortrag

Freitag, 5. April 2019, 10:00–10:15, H22

Ground state splitting and robust braiding of parafermions in fractional quantum hall states — •Solofo Groenendijk1, Alessio Calzona1,2, Edvin Idrisov1, Hugo Tschirhart1, and Thomas Schmidt11Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg — 2Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy

Parafermion bound states generalize the exchange statistics of Majorana fermions and can appear as zero-energy bound states by inducing superconductivity in fractional quantum Hall states. It has been shown that braiding them in edge states can be achieved via a series of nucleation and fusion processes, and can be useful for topological quantum computation. We study analytically and numerically the effect of the chemical potential and a finite length on such braiding protocols.

We show using a combination of bosonization and refermionization that a nonzero chemical potential µ can lift the ground state degeneracy by a factor δ EeL cos(µ L/v), where L is the distance between two parafermions, ξ is a correlation length and v the Fermi velocity. This generalizes a previous result which was based on a semi-classical approach. This effect destroys the robustness of the proposed braiding protocols because it causes level crossings during the braiding process.

We investigate those avoided crossings for Z3 parafermions and show that multiple Landau-Zener transitions occur when using conventional braiding protocols even for slow braiding speeds. We mitigate this effect by proposing a new protocol which is robust to these diabatic transitions.

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