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In this work, we use three different numerical techniques to study the chargetransport properties of a system in the two-level SU(2) (2LSU2) regime,obtained from an SU(4) model Hamiltonian by introducing orbital mixing of thedegenerate orbitals via coupling to the leads. SU(4) Kondo physics has beenexperimentally observed, and studied in detail, in Carbon Nanotube QuantumDots. Adopting a two molecular orbital basis, the Hamiltonian is recast into aform where one of the molecular orbitals decouples from the charge reservoir,although still interacting capacitively with the other molecular orbital. Thisbasis transformation explains in a clear way how the charge transport in thissystem turns from double- to single-channel when it transitions from the SU(4)to the 2LSU2 regime. The charge occupancy of these molecular orbitals displaysgate-potential-dependent occupancy oscillations that arise from a competitionbetween the Kondo and Intermediate Valence states. The determination of whetherthe Kondo or the Intermediate Valence state is more favorable, for a specificvalue of gate potential, is assessed by the definition of an energy scale$T_0$, which is calculated through DMRG. We speculate that the calculation of$T_0$ may provide experimentalists with a useful tool to analyze correlatedcharge transport in many other systems. For that, a current work is underway toimprove the numerical accuracy of its DRMG calculation and explore differentdefinitions.

Transport in Carbon Nanotubes: 2LSU(2) regime reveals subtle competition between Kondo and Intermediate Valence states