Abstract
The bounded XYZ spin chain is studied. We construct the vacuum states by the vertex operators of the level one modules of the elliptic algebra, and compact them through a geometric symmetry of the model called the turning symmetry. From these simplified expressions, the “magnetization formula” for magnetizations at a boundary in the bounded chain and in the half-infinite chains is derived. Applying this formula we calculate the spontaneous magnetization at a boundary in the bounded XYZ spin chain.
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