Scaling of conductance through quantum dots with magnetic field

Abstract

Using different techniques, and Fermi-liquid relationships, we calculate the variation with the applied magnetic field (up to second order) of the zero-temperature equilibrium conductance through a quantum dot described by the impurity Anderson model. We focus on the strong-coupling limit U, where U is the Coulomb repulsion and is half the resonant-level width, and consider several values of the dot level energy E d , ranging from the Kondo regime to the intermediate-valence regime F − E d ∼ , where F is the Fermi energy. We have mainly used the density-matrix renormalization group (DMRG) and the numerical renormalization group (NRG) combined with renormalized perturbation theory (RPT). Results for the dot occupancy and magnetic susceptibility from the DMRG and NRG + RPT are compared with the corresponding Bethe ansatz results for U → ∞, showing an excellent agreement once E d is renormalized by a constant Haldane shift. For U < 3 a simple perturbative approach in U agrees very well with the other methods. The conductance decreases with the applied magnetic field for dot occupancies n d ∼ 1 and increases for n d ∼ 0.5 or n d ∼ 1.5 regardless of the value of U . We also relate the energy scale for the magnetic-field dependence of the conductance with the width of the<br />low-energy peak in the spectral density of the dot.