Noncrossing approximation for the anisotropic Kondo model: Charge fluctuations in a quantum box

The noncrossing approximation (NCA) is generalized to the multichannel Kondo-spin Hamiltonian with arbitrary anisotropic exchange couplings and an external magnetic field, and applied—in the framework of Matveev’s mapping—to the charge fluctuations in a single-electron box at the Coulomb blockade. The temperature dependences of the charge step and the capacitance are calculated for a narrow point contact. At low temperatures and close to the degeneracy point, the capacitance line shape exhibits an approximate scaling with $U/\sqrt{T},$ where U is the deviation in gate voltage from the degeneracy point. This scaling relation is proposed as a sharp experimental diagnostic for the non-Fermi-liquid physics of the system at low temperatures. Both the reliability and shortcomings of the Kondo NCA are discussed in detail. Through comparison with poor-man’s scaling, we are able to pinpoint the omission of particle-particle processes as the origin of the NCA flaws. An extended diagrammatic scheme is devised to amend the NCA flaws.