86 research outputs found
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
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
Nonequilibrium electron transport using the density matrix renormalization group
We extended the Density Matrix Renormalization Group method to study the real
time dynamics of interacting one dimensional spinless Fermi systems by applying
the full time evolution operator to an initial state. As an example we describe
the propagation of a density excitation in an interacting clean system and the
transport through an interacting nano structure
Numerical estimation of critical parameters using the Bond entropy
Using a model of spinless fermions in a lattice with nearest neighbor and
next-nearest neighbor interaction we show that the entropy of the reduced two
site density matrix (the bond entropy) can be used as an extremely accurate and
easy to calculate numerical indicator for the critical parameters of the
quantum phase transition when the basic ordering pattern has a two-site
periodicity. The actual behavior of the bond entropy depends on the particular
characteristics of the transition under study. For the Kosterlitz-Thouless type
phase transition from a Luttinger liquid phase to a charge density wave state
the bond entropy has a local maximum while in the transition from the Luttinger
liquid to the phase separated state the derivative of the bond entropy has a
divergence due to the cancelation of the third eigenvalue of the two-site
reduced density matrix.Comment: Accepted for publication in Physical Review
Tracking spin and charge with spectroscopy in spin-polarised 1D systems
We calculate the spectral function of a one-dimensional strongly interacting
chain of fermions, where the response can be well understood in terms of spinon
and holon excitations. Upon increasing the spin imbalance between the spin
species, we observe the single-electron response of the fully polarised system
to emanate from the holon peak while the spinon response vanishes. For
experimental setups that probe one-dimensional properties, we propose this
method as an additional generic tool to aid the identification of spectral
structures, e.g. in ARPES measurements. We show that this applies even to
trapped systems having cold atomic gas experiments in mind.Comment: 5 pages, 4 figure
Length-dependent oscillations of the conductance through atomic chains: The importance of electronic correlations
We calculate the conductance of atomic chains as a function of their length.
Using the Density Matrix Renormalization Group algorithm for a many-body model
which takes into account electron-electron interactions and the shape of the
contacts between the chain and the leads, we show that length-dependent
oscillations of the conductance whose period depends on the electron density in
the chain can result from electron-electron scattering alone. The amplitude of
these oscillations can increase with the length of the chain, in contrast to
the result from approaches which neglect the interactions.Comment: 7 pages, 4 figure
A Hartree-Fock Study of Persistent Currents in Disordered Rings
For a system of spinless fermions in a disordered mesoscopic ring,
interactions can give rise to an enhancement of the persistent current by
orders of magnitude. The increase in the current is associated with a charge
reorganization of the ground state. The interaction strength for which this
reorganization takes place is sample-dependent and the log-averages over the
ensemble are not representative. In this paper we demonstrate that the
Hartree-Fock method closely reproduces results obtained by exact
diagonalization. For spinless fermions subject to a short-range Coulomb
repulsion U we show that due to charge reorganization the derivative of the
persistent current is a discontinuous function of U. Having established that
the Hartree-Fock method works well in one dimension, we present corresponding
results for persistent currents in two coupled chains.Comment: 4 pages, 6 figures, Submitted to Phys. Rev.
Anderson Localization and Polarization
Effects of randomness have supplied fundamental problems in condensed matter
physics and localization due to interference of quantum mechanical electrons
are well studied as the Anderson localization. Although we have well
established understanding of the localization of non-interacting electrons,
information of the correlated electrons with randomness is still missing. It
was mainly due to lack of reliable numerical techniques for the correlated
electrons.
For the one dimensional correlated systems without randomness, lots of
numerical results are collected by the Density Matrix Renormalization Group
(DMRG) method and consistent understanding with analytical predictions has been
achieved. In this paper, we plan to apply DMRG for the random electron systems
by calculating direct responses of the system with electric field. At first,
random systems without interaction are carefully investigated. Then we try to
treat both of interaction and randomness in one dimensional systems
Interplay disorder-interaction in one dimensional quantum models
URL: http://www-spht.cea.fr/articles/S98/116 Compétition entre le désordre et les interactions dans des modèles quantiques unidimensionnels 210th WE-Heraeus Seminar (PILS'98), Berlin, Germany, October 6-9, 1998We show that the crossover from the weak interaction limit towards the strong interaction limit may be accompanied by a delocalization effect in one dimensional disordered quantum models. The spin degrees of freedom are frozen and the spatial wave functions remain symmetric or antisymmetric when the strength of a short range interaction is varied. The study concerns the excited states for two interacting particles and the ground state for a finite density of carriers. First, for two particles in a chain of length , we establish a duality transformation mapping the behavior at weak onto the behavior at strong . For intermediate , the mixing of the one body states and the interaction induced delocalization effect are maximum. Furthermore, if (the one particle localization length), the system becomes weakly chaotic with critical spectral statistics. This weak chaos is related to the multifractality of the interaction matrix. For two particles starting close to each other, localization is reached in two steps. Before the time necessary to propagate over , de-favors the propagation. On the contrary, favors a very slow delocalization after , characterized by a spreading of the center of mass. Similarly, the curvatures of the energy levels with respect to an enclosed magnetic flux decrease as a function of for . The changes of the curvatures can be described by a conductance-like single scaling parameter. Second, using the density renormalization group algorithm, we have studied the ground state energy of a finite density of spinless fermions and its change under twisted boundary conditions. For a large disorder, a charge reorganization is induced by the interaction: When the system becomes instable between the inhomogeneous configuration driven by the random potential (Anderson insulator) and the homogeneous one driven by repulsive interactions (Mott insulator), the ground state sensitivity can be enhanced by orders of magnitude. In contrast, no enhancement occurs at weaker disorder, when there are many particles on a scale . ----- Cet article est une revue des résultats obtenus récemment par les auteurs sur le rôle joué par l'interaction dans des systèmes unidimensionnels désordonnés. La première partie de l'article traite le problème de deux particules en interaction dans un potentiel aléatoire. On montre que les deux particules peuvent se propager de façon cohérente sur une distance beaucoup plus grande que la longueur de localisation d'une particule sans interaction. L'effet de délocalisation maximale se manifeste pour une valeur de l'interaction intermédiaire entre les deux limites et et une transformation de dualité permet de passer d'une limite à l'autre. La structure multifractale des termes d'interaction de l'hamiltonien dans la base des états sans interaction influence la relation entre et et empêche la transition, engendrée par l'interaction, à un régime complètement chaotique. En changeant on parvient à un régime de ``chaos faible'', caractérisé par une statistique spectrale critique intermédiaire entre la statistique de Poisson (systèmes intégrables) et de Wigner (systèmes ergodiques). On montre que l'interaction est favorable au transport quand la longueur de localisation est plus petite que la taille du système et au contraire est défavorable quand . Ceci est montré dans l'étude de la dynamique d'une paire de particules et de la courbure des niveaux énergétiques pour une boucle traversée par un flux d'Aharonov--Bohm. La deuxième partie de l'article étudie les propriétés de l'état fondamental d'un système de fermions sans spin. Des effets importants de délocalisation se manifestent quand le système devient instable entre les configurations limites (isolant d'Anderson) et (isolant de Mott). La réorganisation des charges d'une limite à l'autre s'accompagne d'une grande sensibilité de l'énergie de l'état fondamental quand les conditions de bord de périodiques deviennent antipériodiques. L'article montre que l'effet de délocalisation semble persister à la limite thermodynamique. \hfill{G. Benenti
Do interactions increase or reduce the conductance of disordered electrons? It depends!
We investigate the influence of electron-electron interactions on the
conductance of two-dimensional disordered spinless electrons. By using an
efficient numerical method which is based on exact diagonalization in a
truncated basis of Hartree-Fock states we are able to determine the exact
low-energy properties of comparatively large systems in the diffusive as well
as in the localized regimes. We find that weak interactions increase the d.c.
conductance in the localized regime while they decrease the d.c. conductance in
the diffusive regime. Strong interactions always decrease the conductance. We
also study the localization of single-particle excitations close to the Fermi
energy which turns out to be only weakly influenced by the interactions.Comment: final version as publsihed, 4 pages REVTEX, 6 EPS figures include
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