Absence of Fibonacci anyons in Rydberg chains

2019/09/20 by Anushya Chandran, F. J. Burnell, Fiona J. Burnell +2 · 1 citation
Mathematics · Physics and Astronomy · #Anyon #Cold Atom Physics and Bose-Einstein Condensates #Combinatorics #Excited state #Fibonacci number #Mathematics #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Rydberg atom #Rydberg formula #Topological Materials and Phenomena #Topological quantum computer #cond-mat.quant-gas #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevb.101.075104

published as Phys. Rev. B 101, 075104 (2020) · 10 pages, 5 figures

arxiv created 2019/09/20 · openalex publication_date 2020/02/05 · arxiv updated 2020/02/12 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/06

Abstract

Recent experiments have focused attention on the properties of chains of atoms in which the atoms are either in their ground states or in highly excited Rydberg states which block similar excitations in their immediate neighbors. As the low-energy Hilbert space of such chains is isomorphic to that of a chain of Fibonacci anyons, they have been proposed as a platform for topological quantum computation and for simulating anyon dynamics. We show that generic local operators in the Rydberg chain correspond to nonlocal anyonic operators that do not preserve a topological symmetry of the physical anyons. Consequently, we argue that Rydberg chains do not yield Fibonacci anyons and quantum computation with Rydberg atoms is not topologically protected.

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