The development of a reliable approach allowing for a realistic
description of single-electron transistors (SET) and molecular
junctions is a contemporary theoretical challenge. At low
temperatures, the transport properties of such quantum dot devices are
governed by strong correlations, giving rise to the Kondo physics.
This limit is particularly challenging from the theoretical point of
view: the ground-state of a Kondo system is characterized by the
entanglement between the quantum dot and the free electron gases in
the Kondo cloud, a complex state whose final structure is highly
sensitive to atomistic details of the materials composing the device.
Therefore, an accurate methodology suiting realistic devices is
expected to interface a precise band structure calculation and
many-body calculation yielding properties in strongly coupled regime.
While ab-initio approaches, such as Density-functional Theory (DFT),
are the preferred tool at the disposal of condensed-matter theorists
interested in the electronic structure of complex materials, the pure
DFT route is to be avoided. To date, the few existing approaches for
strongly correlated problems have a limited scope of applicability.
Previous works based on local and quasi-local approximations for the
exchange-correlation functional extracted from the solution of the
model Hamiltonians via exact methods, yield only qualitatively
descriptions of the low-temperature physical properties of
single-electron transistors or molecular junctions. Considering the
non-local nature of the ground-state in the Kondo regime, one does not
expect to recover experimental realizations of strongly coupled
quantum dots by means of local functionals. To tackle this limit,
numerical methods, such as implementations of the
Renormalization-Group (e.g. NRG and DMRG) offer a reliable framework
to diagonalize model Hamiltonians and compute properties along the
crossover from the weak to the strongly coupled regime. Nonetheless,
in order to perform RG calculations accounting for realistic features
of experimental devices (e.g., geometry, band structure and
electron-electron interactions in the electron gases) the model
parameters must be adjusted conveniently. Motivated by this
frustrating dilemma, we propose a novel tool combining the best
ingredients of DFT and RG in a hybrid calculation. Our approach is
founded on RG concepts, namely the universality of the zero-bias
conductance and the low and high temperature fixed points of the
Anderson Hamiltonian. In the present talk, we will present the main
ideas underlying our hybrid method and illustrate its application to a
relatively simple model: a single-electron transistor modeled by an
inhomogeneous Hubbard Hamiltonian. We will show results for the
conductance in the limit of low-temperatures and discuss the potential
of the new approach to study transport in strongly correlated quantum
dots.
