Yuval Weiss

Level coupled to a one-dimensional interacting reservoir : A density matrix renormalization group study

The influence of interactions in a reservoir coupled to a level on the width of the filling as a function of the chemical potential and the position of the level is studied. The density matrix renormalization group (DMRG) method is used to calculate the ground state of a finite-size interacting reservoir, linked to a single state dot. The influence of the interactions in the lead as well as dot-lead interactions is considered. It is found that interactions in the reservoir result in a decrease in the resonance width, while the dot-lead interaction has an opposite effect. These effects are explained within the random phase approximation as an effective change in the inverse compressibility of the reservoir, while the dot-lead interactions renormalize the position of the level.

Interacting resonant level coupled to a Luttinger liquid: Universality of thermodynamic properties

We investigate a model of a single resonant level coupled to the edge of a quantum wire in the Luttinger-liquid phase or to the middle of a chiral Luttinger liquid via both tunneling and a contact interaction. Utilizing the Yuval-Anderson approach, we map this model onto a classical 1D Coulomb gas in which all the details of both the interactions in the lead and the level-lead interaction enter only through the corresponding Fermi-edge singularity exponent, which we explicitly evaluate using the Bethe ansatz solution for a particular model of the lead. Thus the population, dynamical capacitance and level entropy are universal in the sense of being equal for models with interactions differing in magnitude and even in sign. We demonstrate this to hold quantitatively using density matrix renormalization group calculations. Since the Coulomb gas description is of the single-channel Kondo type, we infer that the universality we found implies that Luttinger-liquid physics has no qualitative effect on these properties, in contrast with perturbative results.

Friedel oscillations in disordered quantum wires: Influence of electron-electron interactions on the localization length

The Friedel oscillations caused due to an impurity located at one edge of a disordered interacting quantum wire are calculated numerically. The electron density in the systems ground state is determined using the DMRG method, and the Friedel oscillations data is extracted using the density difference between the case in which the wire is coupled to an impurity and the case where the impurity is uncoupled. We show that the power law decay of the oscillations occurring for an interacting clean 1D samples described by Luttinger liquid theory, is multiplied by an exponential decay term due to the disorder. Scaling of the average Friedel oscillations by this exponential term collapses the disordered samples data on the clean results. We show that the length scale governing the exponential decay may be associated with the Anderson localization length and thus be used as a convenient way to determine the dependence of the localization length on disorder and interactions. The localization length decreases as a function of the interaction strength, in accordance with previous predictions.

Interacting resonant level coupled to a Luttinger liquid: Population vs. density of states

Abstract We consider the problem of a single level quantum dot coupled to the edge of a one-dimensional Luttinger liquid wire by both a hopping term and electron–electron interactions. Using bosonization and Coulomb gas mapping of the Anderson–Yuval type we show that thermodynamic properties of the level, in particular, its occupation, depend on the various interactions in the system only through a single quantity—the corresponding Fermi edge singularity exponent. However, dynamical properties, such as the level density of states, depend in a different way on each type of interaction. Hence, we can construct different models, with and without interactions in the wire, with equal Fermi edge singularity exponents, which have identical population curves, although they originate from very different level densities of states. The latter may either be regular or show a power law suppression or enhancement at the Fermi energy. These predictions are verified to a high degree of accuracy using the density matrix renormalization group algorithm to calculate the dot occupation, and classical Monte Carlo simulations on the corresponding Coulomb gas model to extract the level density of states.

Driving a first order quantum phase transition by coupling a quantum dot to a 1D charge density wave

The ground state properties of a one-dimensional system with particle–hole symmetry, consisting of a gate controlled dot coupled to an interacting reservoir, are explored using the numerical DMRG method. It has previously been shown that the systems thermodynamic properties as a function of the gate voltage in the Luttinger liquid phase are qualitatively similar to the behaviour of a non-interacting wire with an effective (renormalized) dot–lead coupling. Here we examine the thermodynamic properties of the wire in the charge density wave phase, and show that these properties behave quite differently. The number of electrons in the system remains constant as a function of the gate voltage, while the total energy becomes linear. Moreover, by tuning the gate voltage on the dot in the charge density wave phase it is possible to drive the wire through a first order quantum phase transition in which the population of each site in the wire is inverted.

Significant g -factor values of a two-electron ground state in quantum dots with spin-orbit coupling

The magnetization of semiconductor quantum dots in the presence of spin-orbit (SO) coupling and interactions is investigated numerically. When the dot is occupied by two electrons we find that a level crossing between the two lowest many-body eigenstates may occur as a function of the spin-orbit coupling strength. This level crossing is accompanied by a nonvanishing magnetization of the ground state. Using first-order perturbation theory as well as exact numerical diagonalization of small clusters, we show that the tendency of interactions to cause Stoner-type instability is enhanced by the SO coupling. The resulting

Finite doping of a one-dimensional charge density wave: Solitons vs Luttinger liquid charge density

g

Disorder effect on the Friedel oscillations in a one-dimensional Mott insulator

factor can have a significant value and thus may influence

A generation-based particle–hole density-matrix renormalization group study of interacting quantum dots

g

A DMRG study of a level coupled to a 1D interacting lead

-factor measurements. Finally we propose an experimental method by which the predicted phenomenon can be observed.