Anisotropic Spin-1/2 Heisenberg Chain with Open Boundary Conditions

Abstract

We study the exact solution of the XXZ spin-1/2 Heisenberg chain with a boundary magnetic field in the region where the bulk excitations are gapless. It is shown that a bound state is created near the boundary with a total spin $S = 1/2(\pi/\gamma - 1)$ where $\cos\gamma$ is the anisotropy parameter. When $\gamma < \pi/2$ this spin remains underscreened giving rise to non-analytic contributions to the free energy. The IR fixed point is this case belongs to the universality class of the underscreened Kondo model. We argue that the same fixed point appears in the boundary sine-Gordon model when the scaling dimension of the boundary term $1/2 < \Delta < 1$.