Scaling of conductance through quantum dots with magnetic field

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 >> Delta where U is the Coulomb repulsion and Delta is half the resonant-level width, and consider several values of the dot level energy E-d, ranging from the Kondo regime epsilon(F) -E-d >> Lambda to the intermediate-valence regime epsilon(F) -E-d similar to Lambda, where epsilon(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 -> infinity, showing an excellent agreement once E-d is renormalized by a constant Haldane shift. For U < 3 Delta 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) similar to 1 and increases for n(d) similar to 0.5 or n(d) similar to 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 low-energy peak in the spectral density of the dot.