Fortuitous Universality of Bose-Kondo Impurities

TL;DR

This study investigates Bose-Kondo impurities coupled to a 2+1D O(3) CFT, revealing that different spin impurities flow to distinct stable conformal fixed points, demonstrating a phenomenon called fortuitous universality.

Contribution

The paper introduces the concept of fortuitous universality, showing that Bose-Kondo impurities with different spins each flow to unique stable conformal fixed points.

Findings

Impurity spectra are integer-spaced and consistent with defect conformal symmetry.

Different spin impurities flow to distinct stable infrared conformal fixed points.

The fortuitous universality is expected to extend to all spins, including the infinite limit.

Abstract

We use the fuzzy-sphere approach to study the Bose-Kondo impurity problem, namely a spin-$S$ impurity coupled to the $(2+1)$-dimensional $O(3)$ Wilson-Fisher CFT (Heisenberg universality class). We demonstrate that for $S=1/2,1,3/2$ the impurity flows to a distinct stable interacting conformal defect for each $S$. Using large-scale exact diagonalization and density-matrix renormalization group methods, we observe integer-spaced defect spectrum consistent with defect conformal symmetry and compute several low-lying defect primary operators as well as the RG monotonic $g$-function. Our findings show that despite sharing the same symmetry and anomaly, Bose-Kondo impurities flow to distinct stable infrared conformal fixed points, which we refer to as \emph{fortuitous universality}. We expect this fortuitous universality to persist for all $S$, extending to $S\rightarrow\infty$, with each spin-$S$ impurity flowing to its own stable infrared conformal fixed point.