Spectral properties of strongly correlated multi impurity models in the Kondo insulator regime: Emergent coherence, metallic surface states and quantum phase transitions

TL;DR

This paper explores the spectral properties of multi-impurity Kondo insulators, revealing emergent surface metallic states, quantum phase transitions, and the effects of impurities using advanced numerical methods.

Contribution

It introduces a novel application of the numerical renormalization group to study real-space spectra in correlated impurity arrays, confirming theoretical predictions about surface metallicity and quantum phase transitions.

Findings

Surface states remain metallic in arbitrary dimensions.

Spectral functions vanish or stay finite at the Fermi energy depending on predictions.

Kondo holes induce spectral changes across quantum phase transitions.

Abstract

We investigate the real-space spectral properties of strongly-correlated multi-impurity arrays in the Kondo insulator regime. Employing a recently developed mapping onto an effective correlated cluster problem makes the problem accessible to the numerical renormalization group. The evolution of the spectrum as function of cluster size and cluster site is studied. We applied the extended Lieb-Mattis theorem to predict whether the spectral function must vanish at the Fermi energy developing a true pseudo-gap or whether the spectral function remains finite at $\w=0$. Our numerical renormalization group spectra confirm the predictions of the theorem and shows a metallic behavior at the surface of a cluster prevailing in arbitrary spatial dimensions. We present a conventional minimal extension of a particle-hole symmetric Anderson lattice model at $U=0$ that leads to a gapped bulk band but a surface band with mainly $f$-orbital character for weak and moderate hybridization strength. The change in the site-dependent spectra upon introducing a Kondo hole in the center of the cluster are presented as a function of the hole-orbital energy. In particular the spectral signatures across the Kosterlitz-Thouless type quantum phase transition from a singlet to a local moment fixed point are discussed.