"Conductance of low-dimensional strongly correlated systems"
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Our current understanding of out-of-equilibrium strongly correlated
systems is vastly based on perturbative methods which themselves rely
on the adiabatic switching-on of interactions. Recently the
development of time-dependent simulations of quantum systems have led
to major steps in understanding non-equilibrium quantum systems.
In this first part, I will present a numerical approach that combines
both concepts into an adiabatic tracking of an excited state due to an
external perturbation. Specifically we follow adiabatically the
response of a system to a Aharonov-Bohm type magnetic flux and Coulomb
interaction that is adiabatically switched-on. We are able to access
the non-equilibrium regime of a quantum system.
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Determining the conductance of low-dimensional strongly correlated
structures is an experimental and theoretical challenge in particular
with a view to finding conducting molecules one can use as wires to
build more complex nanostructures. A major challenge consists in
obtaining high resolution in energy space for the leads. In the
context of solving the Kondo problem via a numerical renormalization
technique (NRG), Wilson introduced exponentially decaying hopping
terms to model exponentially large leads. This concept has a major
drawback for transport calculations, for instance within the framework
of the embedding method: each weakened link leads to a backscattering
term spoiling the calculations.
In this second part, I will discuss a new type of boundary conditions,
based on integrable impurities, that also increase the effective
system size. Unlike NRG modified boundary conditions these integrable
impurities induce no interfering backscattering. This will be
illustrated by a real time-dynamics study of a Luttinger liquid and
conductance calculations based on the embedding approach by means of
DMRG algorithms.