Theta function solutions of the quantum Knizhnik-Zamolodchikov-Bernard equation for a face model

Peter E. Finch, Robert Andrew Weston, Paul Zinn-Justin

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Abstract

We consider the quantum Knizhnik-Zamolodchikov-Bernard equation for a face model with elliptic weights, the SOS model. We provide explicit solutions as theta functions. On the so-called combinatorial line, in which the model is equivalent to the three-colour model, these solutions are shown to be eigenvectors of the transfer matrix with periodic boundary conditions.

Original languageEnglish
Article number064001
Number of pages26
JournalJournal of Physics A: Mathematical and Theoretical
Volume49
Issue number6
DOIs
Publication statusPublished - 12 Feb 2016

Keywords

  • quantum Knizhnik-Zamolodchikov equation
  • SOS model
  • three-colour model
  • FREE-FIELD CONSTRUCTION
  • ZUMINO-WITTEN MODELS
  • 8-VERTEX MODEL
  • POLYNOMIAL SOLUTIONS
  • BETHE-ANSATZ
  • SPIN CHAINS
  • SOS MODEL
  • XXZ CHAIN
  • LATTICE
  • COMBINATORICS

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