  In this work, we use three different numerical techniques to study the charge
transport properties of a system in the two-level SU(2) (2LSU2) regime,
obtained from an SU(4) model Hamiltonian by introducing orbital mixing of the
degenerate orbitals via coupling to the leads. SU(4) Kondo physics has been
experimentally observed, and studied in detail, in Carbon Nanotube Quantum
Dots. Adopting a two molecular orbital basis, the Hamiltonian is recast into a
form where one of the molecular orbitals decouples from the charge reservoir,
although still interacting capacitively with the other molecular orbital. This
basis transformation explains in a clear way how the charge transport in this
system turns from double- to single-channel when it transitions from the SU(4)
to the 2LSU2 regime. The charge occupancy of these molecular orbitals displays
gate-potential-dependent occupancy oscillations that arise from a competition
between the Kondo and Intermediate Valence states. The determination of whether
the Kondo or the Intermediate Valence state is more favorable, for a specific
value 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 correlated
charge transport in many other systems. For that, a current work is underway to
improve the numerical accuracy of its DRMG calculation and explore different
definitions.
