Few-body nature of Kondo correlated ground states

TL;DR

This paper investigates the nature of Kondo ground states, revealing they are predominantly few-body in character except near quantum critical points, and demonstrates efficient numerical methods for their analysis.

Contribution

The study introduces a method to distinguish few-body from many-body Kondo states using correlation matrix eigenvalues and shows that ground states are mostly few-body, with many-body correlations emerging only near criticality.

Findings

Correlation eigenvalues decay rapidly, indicating few-body character.

Few-body numerical diagonalization converges exponentially fast.

Finite size effects significantly influence the correlation spectrum.

Abstract

The quenching of degenerate impurity states in metals generally induces a long-range correlated quantum state known as the Kondo screening cloud. While a macroscopic number of particles clearly take part in forming this extended structure, assessing the number of truly entangled degrees of freedom requires a careful analysis of the relevant many-body wavefunction. For this purpose, we examine the natural single-particle orbitals that are eigenstates of the single-particle density (correlation) matrix for the ground state of two quantum impurity problems: the interacting resonant level model (IRLM) and the single impurity Anderson model (SIAM). As a simple and general probe for few-body versus many-body character we consider the rate of exponential decay of the correlation matrix eigenvalues towards inactive (fully empty or filled) orbitals. We find that this rate remains large in the physically most relevant region of parameter space, implying a few-body character. Genuine many-body correlations emerge only when the Kondo temperature becomes exponentially small, for instance near a quantum critical point. In addition, we demonstrate that a simple numerical diagonalization of the few-body problem restricted to the Fock space of the most correlated orbitals converges exponentially fast with respect to the number of orbitals, to the true ground state of the IRLM. We also show that finite size effects drastically affect the correlation spectrum, shedding light on an apparent paradox arising from previous studies on short chains.