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Using different techniques, and Fermi-liquid relationships, we calculate thevariation with applied magnetic field (up to second order) of thezero-temperature equilibrium conductance through a quantum dot described by theimpurity Anderson model. We focus on the strong-coupling limit $U \gg \Delta$where $U$ is the Coulomb repulsion and $\Delta$ is half the resonant-levelwidth, and consider several values of the dot level energy $E_d$, ranging fromthe Kondo regime $\epsilon_F-E_d \gg \Delta$ to the intermediate-valence regime$\epsilon_F-E_d \sim \Delta$, where $\epsilon_F$ is the Fermi energy. We havemainly used density-matrix renormalization group (DMRG) and numericalrenormalization group (NRG) combined with renormalized perturbation theory(RPT). Results for the dot occupancy and magnetic susceptibility from DMRG andNRG+RPT are compared with the corresponding Bethe ansatz results for $U\rightarrow \infty$, showing an excellent agreement once $E_d$ is renormalizedby a constant Haldane shift. For $U < 3 \Delta$ a simple perturbative approachin $U$ agrees very well with the other methods. The conductance decreases withapplied magnetic field for dot occupancies $n_d \sim 1$ and increases for $n_d\sim 0.5$ or $n_d \sim 1.5$ regardless of the value of $U$. We also relate theenergy scale for the magnetic-field dependence of the conductance with thewidth of low energy peak in the spectral density of the dot.

Scaling of conductance through quantum dots with magnetic field