Impurity-induced magnetization in three dimensional antiferromagnet at quantum critical point

TL;DR

This paper investigates how a single impurity affects local magnetization in a 3D antiferromagnet near a quantum critical point, revealing power-law decay of spin density and magnetization, and demonstrating spin-charge separation.

Contribution

It provides a detailed analysis of impurity-induced magnetization near the QCP using two methods, and establishes the equivalence to the independent boson model in the large spin limit.

Findings

Spin density decays as 1/r^3 with distance from impurity.

Staggered magnetization decays as 1/r with logarithmic corrections.

Local spin at impurity site approaches zero at the QCP.

Abstract

We consider a single impurity with spin $S$ embedded in a three-dimensional antiferromagnetic system which is close to the quantum critical point (QCP), separating magnetically ordered and disordered phases. Approaching the QCP from the disordered phase we study the spatial distribution of spin density and staggered magnetization induced by the impurity. Using two methods (self-consistent Born approximation and renormalization group) we found a power law decay of the spin density $\propto 1/r^3$, and of the staggered magnetization $\propto 1/r$ with relevant logarithmic corrections. We demonstrate that the local spin at the impurity site $r=0$ approaches to zero at the QCP. We show that in the semiclassical limit of large $S$ the problem is equivalent to the exactly solvable independent boson model. Our results demonstrate existence of spin-charge separation in the three dimensional systems in the vicinity of the QCP.