XXZ chain with a boundary

Abstract

The $\XXZ$ spin chain with a boundary magnetic field $h$ is considered, using the vertex operator approach to diagonalize the Hamiltonian. We find explicit bosonic formulas for the two vacuum vectors with zero particle content. There are three distinct regions when $h\ge 0$, in which the structure of the vacuum states is different. Excited states are given by the action of vertex operators on the vacuum states. We derive the boundary $S$-matrix and present an integral formula for the correlation functions. The boundary magnetization exhibits boundary hysteresis. We also discuss the rational limit, the $\XXX$ model.

LaTeX 38 pages, 3 figures; epsf, epic, eepic. (Minor changes in text, and references added)

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