Correspondence Between the XXZ Model in Roots of Unity and the One-Dimensional Quantum Ising Chain with Different Boundary Conditions

  • R. A. Usmanov
Part of the NATO Science Series book series (NAII, volume 35)

Abstract

We consider the integrable XXZ model with special open boundary conditions that renders its Hamiltonian U q (sl 2) symmetric, and the one-dimensional quantum Ising model with four different boundary conditions. We show that for each boundary condition the Ising quantum chain is exactly given by the Minimal Model of integrable lattice theory LM(3, 4). This last theory is obtained as the result of the quantum group reduction of the XXZ model at anisotropy Δ(q+q −1)/2=√/2, with a number of sites in the latter defined by the type of boundary conditions.

Keywords

Anisotropy 

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • R. A. Usmanov
    • 1
  1. 1.Landau Institute for Theoretical PhysicsChernogolovka, Moscow regionRussia

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