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

TL;DR

This paper investigates boundary impurity effects in an integrable spin chain, revealing novel quantum critical behaviors and the emergence of ghost spins at strong coupling, extending understanding of impurity interactions in quantum spin systems.

Contribution

It introduces a detailed analysis of impurity-induced critical phenomena in an SU(2)-invariant Heisenberg chain, including the novel concept of ghost spins at strong coupling.

Findings

Impurity can be fully, under, or overcompensated depending on coupling strength.

Strong coupling causes impurity spins to split into ghost spins, leading to new critical behaviors.

Different critical behaviors emerge based on the difference |S'-S|.

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