Ghost spins and novel quantum critical behavior in a spin chain with local bond-deformation

Abstract

We study the boundary impurity-induced critical behavior in an integrable SU(2)-invariant model consisting of an open Heisenberg chain of arbitrary spin-$S$ (Takhatajian-Babujian model) interacting with an impurity of spin $\vec{S&#39;}$ located at one of the boundaries. For $S=1/2$ or $S&#39;=1/2$, the impurity interaction has a very simple form $J\vec{S}_1\cdot\vec{S&#39;}$ which describes the deformed boundary bond between the impurity $\vec{S&#39;}$ and the first bulk spin $\vec{S}_1$ with an arbitrary strength $J$. With a weak coupling $0<J<J_0/[(S+S&#39;)^2-1/4]$, the impurity is completely compensated, undercompensated, and overcompensated for $S=S&#39;$, $S>S&#39;$ and $S<S&#39;$ as in the usual Kondo problem. While for strong coupling $J\geq J_0/[(S+S&#39;)^2-1/4]$, the impurity spin is split into two ghost spins. Their cooperative effect leads to a variety of new critical behaviors with different values of $|S&#39;-S|$.