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

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 $\overrightarrow{S^{\mathrm{\prime }}}$ located at one of the boundaries. For $S=1\mathrm{/}2$ or $S^{\mathrm{\prime }}=1\mathrm{/}2$, the impurity interaction has a very simple form $J{\vec{S}}_1\cdot \overrightarrow{S^{\mathrm{\prime }}}$ which describes the deformed boundary bond between the impurity $\overrightarrow{S^{\mathrm{\prime }}}$ and the first bulk spin ${\vec{S}}_1$ with an arbitrary strength $J$. With a weak coupling $0<J<J_0\mathrm{/}[(S+S^{\mathrm{\prime }}{)}^2-1\mathrm{/}4]$, the impurity is completely compensated, undercompensated, and overcompensated for $S=S^{\mathrm{\prime }}$, $S>S^{\mathrm{\prime }}$ and $S<S^{\mathrm{\prime }}$ as in the usual Kondo problem. While for strong coupling $J\ge J_0\mathrm{/}[(S+S^{\mathrm{\prime }}{)}^2-1\mathrm{/}4]$, the impurity spin is split into two ghost spins. Their cooperative effect leads to a variety of new critical behaviors with different values of $\mathrm{\mid }{S}^{\mathrm{\prime }}-S\mathrm{\mid }$.