XXZ chain with a boundary

TL;DR

This paper analyzes the XXZ spin chain with a boundary magnetic field, providing explicit formulas for vacuum states, boundary S-matrix, and correlation functions, revealing boundary hysteresis effects.

Contribution

It introduces explicit bosonic formulas for vacuum states and derives the boundary S-matrix for the XXZ chain with a boundary, including the rational limit to the XXX model.

Findings

Explicit bosonic formulas for vacuum vectors

Boundary S-matrix derived

Boundary magnetization shows hysteresis

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 $h\geq0$, 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.