Renormalization-group approach to the Anderson model of dilute magnetic alloys. II. Static properties for the asymmetric case

Krishnamurthy, H. R.; Wilkins, John W.; Wilson, Kenneth G.

doi:10.1103/physrevb.21.1044

Cited by 619 publications

(587 citation statements)

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“…In this paper, we will explore how the TSK effect changes when a capacitive coupling is included between the dots. We will use the Numerical Renormalization Group (NRG) method [48][49][50] to calculate the transport and thermodynamical properties of the DQD system. We will show that this new ingredient is responsible for dramatic changes in the lowtemperature physics of the system.…”

Section: Introductionmentioning

confidence: 99%

Capacitively coupled double quantum dot system in the Kondo regime

et al. 2011

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A detailed study of the low-temperature physics of an interacting double quantum dot system in a T-shape configuration is presented. Each quantum dot is modeled by a single Anderson impurity and we include an inter-dot electron-electron interaction to account for capacitive coupling that may arise due to the proximity of the quantum dots. By employing a numerical renormalization group approach to a multi-impurity Anderson model, we study the thermodynamical and transport properties of the system in and out of the Kondo regime. We find that the two-stage-Kondo effect reported in previous works is drastically affected by the inter-dot Coulomb repulsion. In particular, we find that the Kondo temperature for the second stage of the two-stage-Kondo effect increases exponentially with the inter-dot Coulomb repulsion, providing a possible path for its experimental observation.

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Section: Introductionmentioning

confidence: 99%

Capacitively coupled double quantum dot system in the Kondo regime

et al. 2011

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“…Our motivation to restrict the study to the symmetric case is not justified by physical considerations, but mainly for the sake of simplicity, restricting the RG flow into a space of 3 effective parameters (Ũ , t c , t d ) only. Doing so, we proceed as Krishna-murthy, Wilkins and Wilson for the Anderson model, studying first the symmetric case 10 before considering later the asymmetric case 11 and its characteristic valence-fluctuation regime.…”

Section: Restriction To the Symmetric Casementioning

confidence: 99%

“…(11). Therefore, in the limit t d → 0, ISIM must exhibit an orbital Kondo effect if the equivalent Anderson model can be reduced to a Kondo model.…”

Section: Equivalent Anderson Model With Magnetic Fieldmentioning

confidence: 99%

“…The Kondo problem refers to the failure of perturbative techniques to describe this minimum. The solution of these models by the NRG algorithm, a non-perturbative technique [9][10][11][12][13] introduced by Wilson, is at the origin of the discovery of universal behaviors which can emerge from many-body effects. Without magnetic field h and with particle-hole symmetry 10 , the Anderson model maps onto the Kondo Hamiltonian if U > πΓ, Γ ∝ t 2 c being the impurity-level width.…”

Section: Anderson Model Kondo Physics Quantum Dots and Universalitymentioning

confidence: 99%

“…In this work, we study how the effective transmission of a nanosystem with perfect leads is renormalized by local interactions acting inside the nanosystem, using the numerical renormalization group (NRG) algorithm [9][10][11][12][13] and an inversionsymmetric interacting model (ISIM). This model describes the scattering of spin-polarized electrons (spinless fermions) by an interacting region (two sites characterized by an inter-site hopping term t d , coupling terms t c and an inter-site repulsion U ).…”

Section: Introductionmentioning

confidence: 99%

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Universal scaling of the quantum conductance of an inversion-symmetric interacting model

Freyn

Pichard

2010

Phys. Rev. B

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We consider quantum transport of spinless fermions in a 1D lattice embedding an interacting region (two sites with inter-site repulsion U and inter-site hopping t d , coupled to leads by hopping terms tc). Using the numerical renormalization group for the particle-hole symmetric case, we study the quantum conductance g as a function of the inter-site hopping t d . The interacting region, which is perfectly reflecting when t d → 0 or t d → ∞, becomes perfectly transmitting if t d takes an intermediate value τ (U, tc) which defines the characteristic energy of this interacting model. When t d < tc √ U , g is given by a universal function of the dimensionless ratio X = t d /τ . This universality characterizes the non-interacting regime where τ = t 2 c , the perturbative regime (U < t 2 c ) where τ can be obtained using Hartree-Fock theory, and the non-perturbative regime (U > t 2 c ) where τ is twice the characteristic temperature TK of an orbital Kondo effect induced by the inversion symmetry. When t d < τ , the expression g(X) = 4(X + X −1 ) −2 valid without interaction describes also the conductance in the presence of the interaction. To obtain those results, we map this spinless model onto an Anderson model with spins, where the quantum impurity is at the end point of a semi-infinite 1D lead and where t d plays the role of a magnetic field h. This allows us to describe g(t d ) using exact results obtained for the magnetization m(h) of the Anderson model at zero temperature. We expect this universal scaling to be valid also in models with 2D leads, and observable using 2D semi-conductor heterostructures and an interacting region made of two identical quantum dots with strong capacitive inter-dot coupling and connected via a tunable quantum point contact.

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Full-CI quantum chemistry using the density matrix renormalization group

Daul

Ciofini

Daul

et al. 2000

Int. J. Quantum Chem.

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We describe how density-matrix renormalization group (DMRG) can be used to solve the full-CI problem in quantum chemistry. As an illustration of the potential of this method, we apply it to a paramagnetic molecule. In particular, we show the effect of various basis set, the scaling as the fourth power of the size of the problem, and compare the DMRG with other methods. I. INTRODUCTIONFirst-principle quantum chemistry is employed successfully to obtain thermochemical data; molecular structures; force fields and frequencies; assignments of NMR-, photoelectron-, E.S.R-, and UV-spectra; transition state structures as well as activation barriers; dipole moments and other one-or two-electron properties. Two routes of calculation are available: (i) ab initio Hartree-Fock (HF) and post-HF methods; and (ii) density functional theory (DFT). Though both approaches are rigorous, the former one necessitates lengthy configuration interaction (CI) treatment to account for electron correlation; whereas the latter one crucially depends upon the quest for accurate exchange and correlation functionals. The recently acquired popularity of DFT stems in large measure from its computational efficiency, allowing it to treat medium to large size molecules at a fraction of the time required for HF or post-HF calculations. More importantly, expectation values derived from DFT are, in most cases, better in line with experiment than results obtained from HF calculations. This is particularly the case for systems involving transition metals. Nevertheless, if one wants to achieve experimental accuracy for small polyatomic molecules, the method reaches its limits. On the other hand, post-HF overcomes these limits and goes even beyond experimental accuracy, e.g. in case of H 2 . The drawback is of course its very high cost in computational power. However these very accurate calculations of small systems may provide the best route to obtaining more accurate exchange-correlation potentials using the constrained search algorithm of Levy [1].Keeping the discussion to ab initio (HF and post-HF) quantum chemistry, let us now consider the state of the art in this topic. We now know how to do very large calculations, using the direct methodology [2]. We can also manage to work with good basis sets for such calculations, although it is considered that 6-31G* are not good enough, and probably something nearer to TZ2P is required for definitive SCF calculations. Beyond SCF there are major difficulties, all associated with trying to more accurately represent the electron-electron cusp. We know from the work of Kutzelnigg [3], that the convergence of this problem is very slow, something like (ℓ + 1 2 ) −4 , with ℓ the orbital angular momentum quantum number. This means that very large basis sets are required for correlated calculations. We know that it is more important to include d and f basis functions than to improve the methodology (e.g. 6-31G* basis are not appropriate for correlated studies). We also know that the raw cost of the main correlated method...

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Renormalization-group approach to the Anderson model of dilute magnetic alloys. II. Static properties for the asymmetric case

Cited by 619 publications

References 10 publications

Capacitively coupled double quantum dot system in the Kondo regime

Capacitively coupled double quantum dot system in the Kondo regime

Universal scaling of the quantum conductance of an inversion-symmetric interacting model

Full-CI quantum chemistry using the density matrix renormalization group

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