Field-Enhanced Kondo Correlations in a Half-Filling Nanotube Dot: Evolution of an SU(N) Fermi-Liquid Fixed Point

We theoretically study an emergent SU(2) symmetry which is suggested by recent magneto-transport measurements, carried out near two electrons filling of a carbon nanotube quantum dot. It emerges in the case where the spin and orbital Zeeman splittings cancel each other out for two of the one-particle dot levels among four. Using the Wilson numerical renormalization group, we show that a crossover from the SU(4) to SU(2) Fermi-liquid behavior occurs at two impurity-electrons filling as magnetic field increases. We also find that the quasiparticles are significantly renormalized as the remaining two one-particle levels move away from the Fermi level and are frozen at high magnetic fields. In order to clarify how the ground state evolves during such a crossover, we also reexamine the SU(N) Kondo singlet state for M impurity-electrons filling in the limit of strong exchange interactions. We show that the nondegenerate Fermi-liquid fixed point of Nozi\`{e}es and Blandin can be described as a bosonic Perron-Frobenius vector for M hard-core bosons, each of which consists of one impurity-electron and one conduction hole. This interpretation can also be applied to the Fermi-liquid fixed-point without the SU(N) symmetry.