Quantum Geometric Kondo Cloud

Abstract

A magnetic impurity embedded in a metal is collectively screened by Fermi-surface quasiparticles into a many-body spin-singlet ground state, forming a Kondo cloud of size ${\xi }_{\mathrm{K}}\sim \hslash v_F/(k_B{T}_{\mathrm{K}})$. This kinematic picture collapses in flat bands, where $v_F=0$ and the hierarchy of dispersive energy shells is absent. Here we show that the missing organizing principle is quantum geometry. A magnetic impurity coupled to an isolated flat band selects a single active bath mode: a coherent superposition of flat-band Bloch states weighted by the hybridization factor $v(\mathbf{k})$, while all orthogonal flat-band modes remain dark. The resulting flat-band Kondo problem is a quantum geometric molecule, with an algebraic Kondo scale set by the total projected hybridization strength rather than a logarithmic-renormalization scale. In real space, the impurity-bath spin correlation defines a quantum geometric Kondo cloud. Its cloud-size tensor admits a gauge-invariant decomposition into a hybridization-weighted quantum metric, a dressed Berry-connection covariance, and a positive hybridization-gradient term, yielding the lower bound ${\xi }_{\mathrm{K}}^2\ge {\sum }_{\mathbf{k}}\rho (\mathbf{k})\mathrm{Tr}g(\mathbf{k})$, where $\rho (\mathbf{k})=|v(\mathbf{k}){|}^2/{\sum }_{\mathbf{k}}|v(\mathbf{k}){|}^2$. Our result reveals that, in flat bands, Kondo screening is governed by the quantum geometry and interference structure of the impurity-selected Bloch wave packet, rather than Fermi-surface kinematics.

7 pages, 3 figures