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Bosonic matrix product state description of Read-Rezayi states and its application to quasihole spins

Alexander Fagerlund* and Eddy Ardonne†

  • Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden

  • *Contact author: alexander.fagerlund@fysik.su.se
  • †Contact author: ardonne@fysik.su.se
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Phys. Rev. B 112, 125126 – Published 12 September, 2025

DOI: https://doi.org/10.1103/pgsb-wjts

Abstract

We study the k=3 Read-Rezayi quantum Hall state by means of a purely bosonic matrix product state formulation, as described in detail. We calculate the density profiles in the presence of bulk quasiholes of six different types: one for each Z3 parafermion sector. From the density profiles, we calculate the (local) spins of these quasiholes. By employing a spin-statistics relation, we obtain the exchange statistics parameters. Our results, which are entirely based on local properties of the quasiholes, corroborate previous results obtained by explicitly braiding quasiholes, showing that the exchange statistics can be read off from the monodromy properties of the wave functions, i.e., the associated Berry phase vanishes. We also discuss the entanglement spectrum, to show that our bosonic matrix product state formulation correctly captures the Z3 parafermionic structure of the k=3 Read-Rezayi states.

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Phys. Rev. B 112, 125126– Published 12 September, 2025
  • Received 9 January 2025
  • Revised 3 July 2025
  • Accepted 21 August 2025
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