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physica status solidi (b)

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

Yuval Weiss, Miri Sade, Moshe Goldstein, Richard Berkovits

Published Dec 8, 2005• 3 citations
Publisher

Abstract

Abstract The influence of nearest neighbor interactions in a reservoir coupled to a single level dot on the width of the level is studied, using the density matrix renormalization group (DMRG) method. We find that while in the Luttinger liquid (LL) phase of the lead (i.e., for weak interactions) the interactions cause a gradual decrease of the resonance width, in the charge density wave (CDW) phase (for strong interactions) the width is zero, and a sharp jump of the dot population occurs. We explain the physical difference between both cases. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200562749

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Abstract The influence of nearest neighbor interactions in a reservoir coupled to a single level dot on the width of the level is studied, using the density matrix renormalization group (DMRG) method. We find that while in the Luttinger liquid (LL) phase of the lead (i.e., for weak interactions) the interactions cause a gradual decrease of the resonance width, in the charge density wave (CDW) phase (for strong interactions) the width is zero, and a sharp jump of the dot population occurs. We explain the physical difference between both cases. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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.
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.
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.
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.
An interacting spinless fermion wire coupled to a three-dimensional (3D) semiconducting substrate is approximated by a narrow ladder model (NLM) with varying number of legs. We compute density distributions, gaps, charge density wave (CDW) order parameters, correlation functions, and the central charge using the density-matrix renormalization group method. Three ground-state phases are observed: a one-component Luttinger liquid, a quasi-one-dimensional (1D) CDW insulator, and a band insulator. We investigated the convergence of the NLM properties with increasing number of legs systematically and confirm that the NLM is a good approximation for the quasi-1D phases (Luttinger liquid and CDW) of the 3D wire-substrate model. The quantum phase transitions between these phases are investigated as function of the coupling between wire and substrate. The critical nearest-neighbor interaction increases with increasing coupling between wire and substrate and thus the substrate stabilizes the Luttinger liquid in the wire. Our study confirms that a Luttinger liquid or CDW insulator phase could occur in the low-energy properties of atomic wires deposited on semiconducting substrates.
We report the existence of a charge density wave (CDW) in the ground state of the one-dimensional (1D) Kondo lattice model at the filling of n=0.75n=0.75n=0.75 in the weak-coupling region. The CDW is driven by the effective Coulomb repulsion induced by the localized spins. Based on our numerical results using the density matrix renormalization-group method, we show that the CDW phase appears in the paramagnetic region previously known as the Tomonaga-Luttinger liquid. The emergence of this phase serves as an example of a CDW phase induced without bare repulsive interactions, and it enriches the phase diagram of the 1D Kondo lattice model.