Exact Hamiltonian for non-Abelian quasiparticle states

ORAL

Abstract

Non-Abelian anyons have been predicted to emerge in the 5/2 fractional quantum Hall effect. Here, we propose a model Hamiltonian that is exactly solvable for non-Abelian quasiparticles (QPs) as well as quasiholes (QHs). Motivated by the bipartite composite fermion theory [1,2], we construct interactions in terms of two- and three-body Haldane's pseudopotentials. The QP and QH states exhibit the same counting for edge excitations, implying that they obey the same non-Abelian statistics. Our model provides exact solutions for neutral excitations as well. We demonstrate adiabatic continuity for the neutral excited states as we deform our Hamiltonian into the lowest Landau level Hamiltonian with a three-body interaction.

[1] G. J. Sreejith, C. Töke, A. Wójs, and J. K. Jain, Phys. Rev. Lett. 107, 086806 (2011)

[2] I. D. Rodriguez, A. Sterdyniak, M. Hermanns, J. K. Slingerland, and N. Regnault, Phys. Rev. B 85, 035128 (2012)

*K.K. thanks JSPS for support from Overseas Research Fellowship. A.S. and J.K.J acknowledge financial support from the U.S. National Science Foundation under grant no. DMR-2037990. G.J.S. thanks DST-SERB (India) grant ECR/2018/001781 for financial support.

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Publication: K. Kudo, A. Sharma, G. J. Sreejith, and J. K. Jain, arXiv:2206.07789

Presenters

  • Koji Kudo

    • Pennsylvania State University

Authors

  • Koji Kudo

    • Pennsylvania State University

  • Anirban Sharma

    • Pennsylvania State University

  • G. J. Sreejith

    • Indian Institute of Science Education and Research, Pune

  • Jainendra K Jain

    • Pennsylvania State University