Spontaneous Magnetization in the Bounded XXZ Spin Chain

The bounded XXZ spin chain is studied. The operator appeared in the q -difference equation discovered by Cherednik is modified into the transfer matrix of the model. Its eigenstate is composed by the vertex operators of the quantum affine algebra. By use of a geometric symmetry called the “turning symmetry” that the spin chain without boundary magnetic fields satisfies, the asymptotic form of the eigenstate is found and the spontaneous magnetization at a boundary is calculated. It is roughly twice as large as that in the half-infinite XXZ spin chain.

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