Entanglement spectroscopy of non-Abelian anyons: Reading off quantum dimensions of individual anyons

Eyal Cornfeld, L. Aviad Landau, Kirill Shtengel, and Eran Sela
Phys. Rev. B 99, 115429 – Published 20 March 2019

Abstract

We study the entanglement spectrum of topological systems hosting non-Abelian anyons. Akin to energy levels of a Hamiltonian, the entanglement spectrum is composed of symmetry multiplets. We find that the ratio between different eigenvalues within one multiplet is universal and is determined by the anyonic quantum dimensions. This result is a consequence of the conservation of the total topological charge. For systems with non-Abelian topological order, this generalizes known degeneracies of the entanglement spectrum, which are hallmarks of topological states. Experimental detection of these entanglement spectrum signatures may become possible in Majorana wires using multicopy schemes, allowing the measurement of quantum entanglement and its symmetry resolution.

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  • Received 16 October 2018
  • Revised 4 March 2019

DOI:https://doi.org/10.1103/PhysRevB.99.115429

©2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Eyal Cornfeld1,2, L. Aviad Landau1, Kirill Shtengel3, and Eran Sela1,4

  • 1Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel Aviv 6997801, Israel
  • 2Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
  • 3Department of Physics and Astronomy, University of California, Riverside, California 92511, USA
  • 4Department of Physics and Astronomy and Quantum Materials Institute, University of British Columbia, Vancouver, B.C., V6T 1Z1, Canada

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Issue

Vol. 99, Iss. 11 — 15 March 2019

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