Correspondence between the XXZ model in roots of unity and the one-dimensional quantum Ising chain with different boundary conditions

Details Correspondence between the XXZ model in roots of unity and the one-dimensional quantum Ising chain with different boundary conditions Correspondence between the XXZ model in roots of unity and the one-dimensional quantum Ising chain with different boundary conditions

2000-07-19

arxiv.org/abs/hep-th/0007151v4

J.Phys.A34:211-226,2001

Physics

High Energy Physics

High Energy Physics - Theory

23 pages,LaTeX,3 tables,corrected some typos

Scientific paper

10.1088/0305-4470/34/2/301

We consider the integrable XXZ model with special open boundary conditions that renders its Hamiltonian ${SU(2)}_q$ 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 $\Delta=(q + q^{-1})/2=\sqrt{2}/2$, with a number of sites in the latter defined by the type of boundary conditions.

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