Crossover in the two-impurity Kondo model induced by direct charge tunneling

TL;DR

This paper investigates how direct charge tunneling induces a crossover in the two-impurity Kondo model, analyzing the critical behavior and low-energy fixed points through renormalization group methods and numerical simulations.

Contribution

It provides a derivation of the crossover scale T* using renormalization group analysis and confirms it with numerical renormalization group calculations, elucidating the low-energy fixed point structure.

Findings

Derivation of the crossover scale T* from RG analysis.

Confirmation of T* and fixed point form via NRG.

Implications for double quantum dot systems.

Abstract

Quantum critical behavior in the two-impurity Kondo model requires the distinct separation of two scales, T_K >> T*, where T_K is the Kondo temperature and T* is the scale at which the system renormalizes away from the quantum critical point to a stable Fermi liquid fixed point. We provide a derivation of T* based on the renormalization group to lowest order. This result is confirmed by a numerical renormalization group (NRG) analysis which supplements the analytic derivation with additional quantitative precision. The form of the low-energy Fermi liquid fixed point is derived and subsequently confirmed by the NRG. We discuss implications for series double quantum dot systems.