Quantum phase transition in a gapped Anderson model: A numerical renormalization group study

TL;DR

This study uses numerical renormalization group techniques to analyze how a gapped conduction band affects the quantum phase transition and spectral properties of a single-impurity Anderson model, revealing a transition from Kondo to localized moment states.

Contribution

It provides a detailed numerical analysis of the quantum phase transition induced by a gap in the Anderson model, highlighting the evolution of bound states and spectral features.

Findings

Quantum phase transition occurs as a function of the gap size.

Bound states form differently in strong-coupling and localized regimes.

Spectral properties change significantly across the transition.

Abstract

We use the numerical renormalization group method to investigate the spectral properties of a single-impurity Anderson model with a gap {\delta} across the Fermi level in the conduction-electron spectrum. For any finite {\delta} > 0, at half filling the ground state of the system is always a doublet. Away from half filling a quantum phase transition (QPT) occurs as function of the gap value {\delta}, and the system evolves from the strong-coupling (SC) Kondo-type state, corresponding to {\delta} <{\delta}_C toward a localized moment (LM) regime for {\delta} > {\delta}_C. The opening of the gap leads to the formation of one (two) bound states when the system is in the SC (LM) regime. The evolution across the QPT of their positions and the corresponding weights together with the dynamic properties of the model are investigated.