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Annales Henri Poincaré

, Volume 16, Issue 5, pp 1103–1153 | Cite as

On the Form Factors of Local Operators in the Bazhanov–Stroganov and Chiral Potts Models

  • Nicolas Grosjean
  • Jean-Michel MailletEmail author
  • Giuliano Niccoli
Article

Abstract

We consider general cyclic representations of the six-vertex Yang–Baxter algebra and analyze the associated quantum integrable systems, the Bazhanov–Stroganov model and the corresponding chiral Potts model on finite size lattices. We first determine the propagator operator in terms of the chiral Potts transfer matrices and we compute the scalar product of separate states (including the transfer matrix eigenstates) as a single determinant formulae in the framework of Sklyanin’s quantum separation of variables. Then, we solve the quantum inverse problem and reconstruct the local operators in terms of the separate variables. We also determine a basis of operators whose form factors are characterized by a single determinant formulae. This implies that the form factors of any local operator are expressed as finite sums of determinants. Among these form factors written in determinant form are in particular those which will reproduce the chiral Potts order parameters in the thermodynamic limit. The results presented here are the generalization to the present models associated to the most general cyclic representations of the six-vertex Yang–Baxter algebra of those we derived for the lattice sine–Gordon model.

Keywords

Form Factor Transfer Matrix Local Operator Heisenberg Chain Determinant Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Nicolas Grosjean
    • 1
  • Jean-Michel Maillet
    • 2
    Email author
  • Giuliano Niccoli
    • 2
  1. 1.LPTM, UMR 8089 du CNRSUniversité de Cergy-PontoiseCergy-PontoiseFrance
  2. 2.Laboratoire de PhysiqueUMR 5672 du CNRS, ENS LyonLyonFrance

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