40 research outputs found
Shot noise in the self-dual Interacting Resonant Level Model
By using two independent and complementary approaches, we compute exactly the
shot noise in an out-of-equilibrium interacting impurity model, the Interacting
Resonant Level model at its self-dual point. An analytical approach based on
the Thermodynamical Bethe Ansatz allows to obtain the density matrix in the
presence of a bias voltage, which in turn allows for the computation of any
observable. A time-dependent Density Matrix Renormalization Group technique,
that has proven to yield the correct result for a free model (the Resonant
Level Model) is shown to be in perfect agreement with the former method.Comment: 4 pages, 3 figure
Numerical Evaluation of Shot Noise using Real Time Simulations
We present a method to determine the shot noise in quantum systems from
knowledge of their time evolution - the latter being obtained using numerical
simulation techniques. While our ultimate goal is the study of interacting
systems, the main issues for the numerical determination of the noise do not
depend on the interactions. To discuss them, we concentrate on the single
resonant level model, which consists in a single impurity attached to
non-interacting leads, with spinless fermions. We use exact diagonalisations
(ED) to obtain time evolution, and are able to use known analytic results as
benchmarks. We obtain a complete characterization of finite size effects at
zero frequency, where we find that the finite size corrections scale , the differential conductance. We also discuss finite frequency noise,
as well as the effects of damping in the leads.Comment: 6 pages, 7 figure
Non-equilibrium electronic transport in a one-dimensional Mott insulator
We calculate the non-equilibrium electronic transport properties of a
one-dimensional interacting chain at half filling, coupled to non-interacting
leads. The interacting chain is initially in a Mott insulator state that is
driven out of equilibrium by applying a strong bias voltage between the leads.
For bias voltages above a certain threshold we observe the breakdown of the
Mott insulator state and the establishment of a steady-state electronic current
through the system. Based on extensive time-dependent density matrix
renormalization group simulations, we show that this steady-state current
always has the same functional dependence on voltage, independent of the
microscopic details of the model and relate the value of the threshold to the
Lieb-Wu gap. We frame our results in terms of the Landau-Zener dielectric
breakdown picture. Finally, we also discuss the real-time evolution of the
current, and characterize the current-carrying state resulting from the
breakdown of the Mott insulator by computing the double occupancy, the spin
structure factor, and the entanglement entropy.Comment: 12 pages RevTex4, 12 eps figures, as published, minor revision
Exact time-dependent density functional theory for impurity models
We employ the density matrix renormalization group to construct the exact
time-dependent exchange correlation potential for an impurity model with an
applied transport voltage. Even for short-ranged interaction we find an
infinitely long-ranged exchange correlation potential which is built up
{instantly} after switching on the voltage. Our result demonstrates the
fundamental difficulties of transport calculations based on time-dependent
density functional theory. While formally the approach works, important
information can be missing in the ground-state functionals and may be hidden in
the usually unknown non-equilibrium functionals
Numerical method for non-linear steady-state transport in one-dimensional correlated conductors
We present a method for investigating the steady-state transport properties
of one-dimensional correlated quantum systems. Using a procedure based on our
analysis of finite-size effects in a related classical model (LC line) we show
that stationary currents can be obtained from transient currents in finite
systems driven out of equilibrium. The non-equilibrium dynamics of correlated
quantum systems is calculated using the time-evolving block decimation method.
To demonstrate our method we determine the full I-V characteristic of the
spinless fermion model with nearest-neighbour hopping t_H and interaction V_H
using two different setups to generate currents (turning on/off a potential
bias). Our numerical results agree with exact results for non-interacting
fermions (V_H=0). For interacting fermions we find that in the linear regime eV
<< 4t_H the current I is independent from the setup and our numerical data
agree with the predictions of the Luttinger liquid theory combined with the
Bethe Ansatz solution. For larger potentials V the steady-state current depends
on the current-generating setup and as V increases we find a negative
differential conductance with one setup while the currents saturate at finite
values in the other one. Both effects are due to finite renormalized
bandwidths.Comment: published versio
Embedding method for the scattering phase in strongly correlated quantum dots
The embedding method for the calculation of the conductance through
interacting systems connected to single channel leads is generalized to obtain
the full complex transmission amplitude that completely characterizes the
effective scattering matrix of the system at the Fermi energy. We calculate the
transmission amplitude as a function of the gate potential for simple
diamond-shaped lattice models of quantum dots with nearest neighbor
interactions. In our simple models we do not generally observe an interaction
dependent change in the number of zeroes or phase lapses that depend only on
the symmetry properties of the underlying lattice. Strong correlations separate
and reduce the widths of the resonant peaks while preserving the qualitative
properites of the scattering phase.Comment: 11 pages, 3 figures. Proceedings of the Workshop on Advanced
Many-Body and Statistical Methods in Mesoscopic Systems, Constanta, Romania,
June 27th - July 2nd 2011. To appear in Journal of Physics: Conference Serie
Nonlinear Transport through Quantum Dots Studied by the Time-Dependent DMRG
Recent developments on studies of transport through quantum dots obtained by
applying the time-dependent density matrix renormalization group method are
summarized. Some new aspects of Kondo physics which appear in nonequilibrium
steady states are discussed both for the single dot case and for the serially
coupled double-quantum-dot case.Comment: 8 pages, 15 figure
Time-dependent bond-current functional theory for lattice Hamiltonians: fundamental theorem and application to electron transport
The cornerstone of time-dependent (TD) density functional theory (DFT), the
Runge-Gross theorem, proves a one-to-one correspondence between TD potentials
and TD densities of continuum Hamiltonians. In all practical implementations,
however, the basis set is discrete and the system is effectively described by a
lattice Hamiltonian. We point out the difficulties of generalizing the
Runge-Groos proof to the discrete case and thereby endorse the recently
proposed TD bond-current functional theory (BCFT) as a viable alternative.
TDBCFT is based on a one-to-one correspondence between TD Peierl's phases and
TD bond-currents of lattice systems. We apply the TDBCFT formalism to
electronic transport through a simple interacting device weakly coupled to two
biased non-interacting leads. We employ Kohn-Sham Peierl's phases which are
discontinuous functions of the density, a crucial property to describe Coulomb
blockade. As shown by explicit time propagations, the discontinuity may prevent
the biased system from ever reaching a steady state.Comment: 11 pages, 7 figure