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arXiv:cond-mat/0306284

Density matrix renormalization group study of the charging of a quantum dot strongly coupled to a single lead

Richard Berkovits

Published Jun 11, 2003• 0 citations
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Abstract

A new application of the density matrix renormalization group (DMRG) method to a system composed of an interacting dot coupled to a infinite one dimensional lead is presented. This method enables one to study the influence of the coupling to an external lead on the thermodynamical properties of the dot. It is shown that this method reproduces known results for a non-interacting dot coupled to a lead, i.e., that for strong coupling discrete states remain in the dot. We show that these states are robust and do not disappear once interactions in the dot are considered. Moreover, due to these discrete states, Coulomb blockade affects the charging of the dot even though its strongly coupled to a lead.

DOI
10.48550/arxiv.cond-mat/0306284

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A new application of the density matrix renormalization group (DMRG) method to a system composed of an interacting dot coupled to a infinite one dimensional lead is presented. This method enables one to study the influence of the coupling to an external lead on the thermodynamical properties of the dot. It is shown that this method reproduces known results for a non-interacting dot coupled to a lead, i.e., that for strong coupling discrete states remain in the dot. We show that these states are robust and do not disappear once interactions in the dot are considered. Moreover, due to these discrete states, Coulomb blockade affects the charging of the dot even though its strongly coupled to a lead.
The influence of weak 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 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.
A new method to perform linear and finite bias conductance calculations in one dimensional systems based on the calculation of real time evolution within the Density Matrix Renormalization Group (DMRG) is presented. We consider a system of spinless fermions consisting of an extended interacting nanostructure attached to non-interacting leads. Results for the linear and finite bias conductance through a seven site structure with weak and strong nearest-neighbor interactions are presented. Comparison with exact diagonalization results in the non-interacting limit serve as verification of the accuracy of our approach. Our results show that interaction effects lead to an energy dependent self energy in the differential conductance.
Abstract. The numerical renormalization group is employed to study a double quantum (DQD) dot system consisting of two equivalent single-level dots, each coupled to its own lead and with a mutual capacitive coupling embodied in an interdot interaction U ′, in addition to the intradot Coulomb interaction U. We focus on the regime with two electrons on the DQD, and the evolution of the system on increasing U ′/U. The spin-Kondo effect arising for U ′ = 0 (SU(2) × SU(2)) is found to persist robustly with increasing U ′/U, before a rapid but continuous crossover to (a) the SU(4) point U ′ = U where charge and spin degrees of freedom are entangled and the Kondo scale strongly enhanced; and then (b) a charge-Kondo state, in which a charge-pseudospin is quenched on coupling to the leads/conduction channels. A quantum phase transition of Kosterlitz-Thouless type then occurs from this Fermi liquid, strong coupling (SC) phase, to a broken symmetry, non-Fermi liquid charge ordered (CO) phase at a critical U ′ c. Our emphasis in this paper is on the structure, stability and flows between the underlying RG fixed points, on the overall phase diagram in the (U, U ′)-plane and evolution of the characteristic low-energy Kondo scale inherent to the SC phase; and on static physical properties such as spin- and charge-susceptibilities (staggered and uniform), including universality and scaling behaviour in the strongly correlated regime. Some exact results for associated Wilson ratios are also obtained.
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 system's 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.
The numerical renormalization group is employed to study a double quantum (DQD) dot system consisting of two equivalent single-level dots, each coupled to its own lead and with a mutual capacitive coupling embodied in an interdot interaction U', in addition to the intradot Coulomb interaction U. We focus on the regime with two electrons on the DQD, and the evolution of the system on increasing U'/U. The spin-Kondo effect arising for U'=0 (SU(2) x SU(2)) is found to persist robustly with increasing U'/U, before a rapid but continuous crossover to (a) the SU(4) point U'=U where charge and spin degrees of freedom are entangled and the Kondo scale strongly enhanced; and then (b) a charge-Kondo state, in which a charge-pseudospin is quenched on coupling to the leads/conduction channels. A quantum phase transition of Kosterlitz-Thouless type then occurs from this Fermi liquid, strong coupling (SC) phase, to a broken symmetry, non-Fermi liquid charge ordered (CO) phase at a critical U'_c. Our emphasis in this paper is on the structure, stability and flows between the underlying RG fixed points, on the overall phase diagram in the (U,U')-plane and evolution of the characteristic low-energy Kondo scale inherent to the SC phase; and on static physical properties such as spin- and charge-susceptibilities (staggered and uniform), including universality and scaling behaviour in the strongly correlated regime. Some exact results for associated Wilson ratios are also obtained.
A quantum dot coupled to ferromagnetically polarized one-dimensional leads is studied numerically using the density-matrix renormalization group method. Several real space properties and the local density of states at the dot are computed. It is shown that this local density of states is suppressed by the parallel polarization of the leads. In this case we are able to estimate the length of the Kondo cloud, and to relate its behavior to that suppression. Another important result of our study is that the tunnel magnetoresistance as a function of the quantum dot on-site energy is minimum and negative at the symmetric point.