Single-Particle and Magnetic Excitation Spectra of Degenerate Anderson Model with Finite<i>f</i>–<i>f</i>Coulomb Interaction

Sakai, Osamu; Shimizu, Yukihiro; Kasuya, T.

doi:10.1143/jpsj.58.3666

Cited by 133 publications

(148 citation statements)

References 30 publications

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“…There is one state with excitation energy E ex → 0 for N → ∞ but its matrix element with the ground state vanishes as N → ∞. In order to obtain the full frequency dependence of the spectral function within the NRG, it is necessary to combine the information of all iteration steps as in each iteration the results are only given for a certain frequency range (see also [16,17]). …”

Section: Results For the Spectral Functionmentioning

confidence: 99%

Anderson impurity in pseudo-gap Fermi systems

Bulla

Pruschke

Hewson

1997

J. Phys.: Condens. Matter

169

352

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We use the numerical renormalization group method to study an Anderson impurity in a conduction band with the density of states varying as ρ(ω) ∝ |ω| r with r > 0. We find two different fixed points: a local-moment fixed point with the impurity effectively decoupled from the band and a strong-coupling fixed point with a partially screened impurity spin. The specific heat and the spin-susceptibility show powerlaw behaviour with different exponents in strong-coupling and localmoment regime. We also calculate the impurity spectral function which diverges (vanishes) with |ω| −r (|ω| r ) in the strong-coupling (local moment) regime.PACS 75.20.Hr

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Section: Results For the Spectral Functionmentioning

confidence: 99%

Anderson impurity in pseudo-gap Fermi systems

Bulla

Pruschke

Hewson

1997

J. Phys.: Condens. Matter

169

352

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“…Let us first describe the procedure for calculating the T = 0 spectral function [20,30]. The diagonalization of the clusters N = 0, 1, 2, .…”

Section: B Finite Temperature Dynamicsmentioning

confidence: 99%

Finite-temperature numerical renormalization group study of the Mott transition

2001

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Wilson's numerical renormalization group (NRG) method for the calculation of dynamic properties of impurity models is generalized to investigate the effective impurity model of the dynamical mean field theory at finite temperatures. We calculate the spectral function and self-energy for the Hubbard model on a Bethe lattice with infinite coordination number directly on the real frequency axis and investigate the phase diagram for the Mott-Hubbard metal-insulator transition. While for T < Tc ≈ 0.02W (W : bandwidth) we find hysteresis with first-order transitions both at Uc1 (defining the insulator to metal transition) and at Uc2 (defining the metal to insulator transition), at T > Tc there is a smooth crossover from metallic-like to insulating-like solutions.71.10. Fd, 71.30.+h

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“…Our work builds on Wilson's numerical renormalization group (NRG) method [1]. Wilson discretized the environmental spectrum on a logarithmic grid of energies Λ −n , (with Λ > 1, 1 ≤ n ≤ N → ∞), with exponentially high resolution of low-energy excitations, and mapped the impurity model onto a "Wilson tight-binding chain", with hopping matrix elements that decrease exponentially as Λ −n/2 with site index n. Because of this separation of energy scales, the Hamiltonian can be diagonalized iteratively: adding one site at a time, a new "shell" of eigenstates is constructed from the new site's states and the M K lowest-lying eigenstates of the previous shell (the so-called "kept" states), while "discarding" the rest.Subsequent authors [2,3,4,5,6,7,8,9,10] have shown that spectral functions such as A BC (ω) can be calculated via the Lehmann sum, using NRG states (kept and discarded) of those shells n for which ω ∼ Λ −n/2 . Though plausible on heuristic grounds, this strategy entails double-counting ambiguities [5] about how to combine data from successive shells.…”

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confidence: 99%

Sum-Rule Conserving Spectral Functions from the Numerical Renormalization Group

2007

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We show how spectral functions for quantum impurity models can be calculated very accurately using a complete set of "discarded" numerical renormalization group eigenstates, recently introduced by Anders and Schiller. The only approximation is to judiciously exploit energy scale separation. Our derivation avoids both the overcounting ambiguities and the single-shell approximation for the equilibrium density matrix prevalent in current methods, ensuring that relevant sum rules hold rigorously and spectral features at energies below the temperature can be described accurately. PACS numbers: 71.27.+a, 75.20.Hr, 73.21.La Quantum impurity models describe a quantum system with a small number of discrete states, the "impurity", coupled to a continuous bath of fermionic or bosonic excitations. Such models are relevant for describing transport through quantum dots, for the treatment of correlated lattice models using dynamical mean field theory, or for the modelling of the decoherence of qubits.The impurity's dynamics in thermal equilibrium can be characterized by spectral functions of the type A BC (ω) = dt 2π e iωt B (t)Ĉ T . Their Lehmann representation readswith Z = a e −βEa and E ba = E b − E a , which implies the sum rule dωA BC (ω) = BĈ T . In this Letter, we describe a strategy for numerically calculating A BC (ω) that, in contrast to previous methods, rigorously satisfies this sum rule and accurately describes both high and low frequencies, including ω T , which we test by checking our results against exact Fermi liquid relations. Our work builds on Wilson's numerical renormalization group (NRG) method [1]. Wilson discretized the environmental spectrum on a logarithmic grid of energies Λ −n , (with Λ > 1, 1 ≤ n ≤ N → ∞), with exponentially high resolution of low-energy excitations, and mapped the impurity model onto a "Wilson tight-binding chain", with hopping matrix elements that decrease exponentially as Λ −n/2 with site index n. Because of this separation of energy scales, the Hamiltonian can be diagonalized iteratively: adding one site at a time, a new "shell" of eigenstates is constructed from the new site's states and the M K lowest-lying eigenstates of the previous shell (the so-called "kept" states), while "discarding" the rest.Subsequent authors [2,3,4,5,6,7,8,9,10] have shown that spectral functions such as A BC (ω) can be calculated via the Lehmann sum, using NRG states (kept and discarded) of those shells n for which ω ∼ Λ −n/2 . Though plausible on heuristic grounds, this strategy entails double-counting ambiguities [5] about how to combine data from successive shells. Patching schemes [9] for addressing such ambiguities involve arbitrariness. As a result, the relevant sum rule is not satisfied rigorously, with typical errors of a few percent. Also, the density matrix (DM)ρ = e −βĤ /Z has hitherto been represented rather crudely using only the single N T -th shell for which, with a chain of length N = N T , resulting in inaccurate spectral information for ω T . In this Letter we avoid these probl...

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Single-Particle and Magnetic Excitation Spectra of Degenerate Anderson Model with Finitef–fCoulomb Interaction

Cited by 133 publications

References 30 publications

Anderson impurity in pseudo-gap Fermi systems

Anderson impurity in pseudo-gap Fermi systems

Finite-temperature numerical renormalization group study of the Mott transition

Sum-Rule Conserving Spectral Functions from the Numerical Renormalization Group

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