Transport in quantum dots from the integrability of the Anderson model

In this work we exploit the integrability of the two-lead Anderson model to compute transport properties of a quantum dot, in and out of equilibrium. Our method combines the properties of integrable scattering together with a Landauer-Buttiker formalism. Although we use integrability, the nature of the problem is such that our results are not generically exact, but must only be considered as excellent approximations which nonetheless are valid all the way through crossover regimes. The key to our approach is to identify the excitations that correspond to scattering states and then to compute their associated scattering amplitudes. We are able to do so both in and out of equilibrium. In equilibrium and at zero temperature, we reproduce the Friedel sum rule for an arbitrary magnetic field. From this we compute exactly the behavior of the zero-temperature linear-response conductance as a function of both the gate voltage and field. We also study transport quantities requiring knowledge of scattering states away from the Fermi surface. We compute the linear-response conductance at finite temperature at the symmetric point of the Anderson model and reproduce the numerical renormalization-group computation of this quantity of Costi We then explore the out-of-equilibrium conductance for a near-symmetric Anderson model and arrive at quantitative expressions for the differential conductance, both in and out of a magnetic field. We reproduce the expected splitting of the differential conductance peak into two in a finite magnetic field H. We determine the width, height, and position of these peaks. In particular, we find that for Hmuch greater thanT(k), the Kondo temperature, the differential conductance has maxima of e(2)/h occurring for a bias V close to but smaller than H. The nature of our construction of scattering states suggests that our results for the differential magnetoconductance are not merely approximate, but become exact in the large-field limit.