Non-Abelian statistics in one dimension: Topological momentum spacings and SU(2) level- k fusion rules

  title={Non-Abelian statistics in one dimension: Topological momentum spacings and SU(2) level-
 fusion rules},
  author={Martin Greiter and F. D. M. Haldane and Ronny Thomale},
  journal={Physical Review B},
We use a family of critical spin chain models discovered recently by one of us [M. Greiter, Mapping of Parent Hamiltonians, Springer, Berlin/Heidelberg 2011] to propose and elaborate that non-Abelian, SU(2) level $k=2S$ anyon statistics manifests itself in one dimension through topological selection rules for fractional shifts in the spacings of linear momenta, which yield an internal Hilbert space of, in the thermodynamic limit degenerate states. These shifts constitute the equivalent to the… 

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  • T. QuellaA. Roy
  • Physics
    Journal of Statistical Mechanics: Theory and Experiment
  • 2020
We construct a family of 1D and 2D long-range SU(2) spin models as parent Hamiltonians associated with infinite dimensional matrix product states that arise from simple current correlation functions

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