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

TL;DR

This paper analyzes the exact solution of the anisotropic spin-1/2 Heisenberg chain with open boundaries, revealing boundary-bound states, non-analytic free energy contributions, and connections to the underscreened Kondo and boundary sine-Gordon models.

Contribution

It provides an exact solution for the boundary effects in the XXZ spin chain and links these to known impurity models, highlighting new boundary fixed points.

Findings

Boundary-bound state with specific spin depending on anisotropy.

Non-analytic contributions to free energy for certain anisotropy ranges.

Identification of boundary fixed points related to the underscreened Kondo model.

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 $1/2 < \Delta < 1$.