Numerical renormalization group calculations for the self-energy of the impurity Anderson model

Bulla, Ralf; Hewson, A. C.; Pruschke, Thomas

doi:10.1088/0953-8984/10/37/021

Cited by 297 publications

(387 citation statements)

References 28 publications

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“…is usually assumed to be constant between the band-edges −D and D, but will acquire some frequency dependence in the effective Anderson model within the DMFT (the necessary changes in the NRG-procedure due to the nonconstant ∆(ω) were discussed in [14,27]). The first step to set up the renormalization group transformation is a logarithmic discretization of the conduction band: the continuous conduction band is divided into infinitely many intervals [ξ n+1 , ξ n ] and [−ξ n , −ξ n+1 ] with ξ n = DΛ −n and n = 0, 1, 2, .…”

Section: A General Conceptsmentioning

confidence: 99%

“…(7-8)) and evaluates the spectral densities at the characteristic frequencies defined above. It is also possible to first combine information on the discrete spectra from successive clusters (N and N + 2, to avoid even/odd effects) and then broaden the spectra [14]. Below, we describe this latter approach, which we used to obtain most results in this paper.…”

Section: B Finite Temperature Dynamicsmentioning

confidence: 99%

“…The above-mentioned restrictions concerning the value of U and T , or the low energy resolution, do not apply to the numerical renormalization group method (NRG) [11,12] which has only recently been used to investigate lattice models within the DMFT [13][14][15][16][17]. The NRG as well has its drawbacks, which will be discussed in Sec.…”

Section: Introductionmentioning

confidence: 99%

“…Applications of the NRG within the DMFT include the investigation of the Mott-transition [13][14][15], the problem of charge ordering in the extended Hubbard model [16], and the formation of the heavy-fermion liquid in the periodic Anderson model [17]. In all these investigations, the temperature was restricted to T = 0.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: A General Conceptsmentioning

confidence: 99%

Section: B Finite Temperature Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite-temperature numerical renormalization group study of the Mott transition

2001

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“…It proved to be very successful in clarifying the low-energy properties of various impurity problems [13,14,15,16,17], and it will be the method of choice for analyzing more complex quantum dot systems.…”

Section: Introductionmentioning

confidence: 99%

Numerical Renormalization Group Analysis of Interacting Quantum Dots

Hofstetter

Advances in Solid State Physics

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Abstract. Wilson's Numerical Renormalization Group (NRG) is so far the only nonperturbative technique that can reliably access low-energy properties of quantum impurity systems. We present a recent extension of the method, the DM-NRG, which yields highly accurate results for dynamical quantities at arbitrary frequencies and temperatures. As an application, we determine the spectrum of a quantum dot in an external magnetic field. Furthermore, we discuss magnetic impurities with orbital degeneracy, which have been inferred in recent experiments on quantum dots in an Aharonov-Bohm geometry. It is demonstrated that for spinless electrons, interference between neighbouring levels sets the low-energy scale of the system. Switching on an external field leads to a remarkable crossover into a regime dominated by orbital Kondo screening. We predict that the broadening-induced level splitting should be clearly visible in measurements of the optical absorption power. A more general model including the electron spin is studied within an extended two-band NRG procedure. We observe competition between interference and Kondo screening, similar to the situation in two-impurity models (RKKY).

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Quasiparticles in transition metals with strong local correlations: band formation and collective effects

Grewe

2005

Ann. Phys.

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We address the question, whether low lying one-particle excitations in the Fermi-liquid phase of highly correlated electron systems can form well defined bands of nearly stable quasiparticles, and comment on features of a universal band picture for these systems. We outline how to derive a description of instabilities to magnetic, charged ordered or superconducting phases, which bears a close analogy to Stoner theory and lends itself to an interpretation in terms of quasiparticle bands and residual interactions at low temperatures. Concepts and problems are illustrated via calculations for some standard models of solid-state theory using modern many-body techniques like NRG, NCA and DMFT. Differences to conventional band structure theory are pointed out. We shortly comment on the relevance of these questions to the physics of inhomogeneous systems and small particles. The quasiparticle concept and bandsLandau's concept of a Fermi liquid [1] has been of great importance for our understanding of various properties of metals, since it reconciles the picture of independent electrons with our knowledge about their interactions and the correlations thereby induced. In simple metals the conduction bands are broad, the kinetic contribution to the energy is important and electrons acquire a moderate dressing only. They bear an apparent correspondence to the quasiparticles, which constitute the Fermi liquid at low temperatures. This concept also applies to systems of a quite different nature, in particular to the He-3 fluid, in which the fundamental Fermions are atoms with stable electron shells interacting dominantly via a strong shortranged force. Here, the quasiparticles differ considerably from these atoms, incorporating strong backflow effects [2]. It came as a surprise that transition metal compounds can host even more extreme types of Fermi liquids [3], with quasiparticles heavier by a factor of thousand than bare electrons [4]. Although the study of exotic groundstates with superconducting or magnetic order originally lay in the main focus of scientific activity [5,6], it seems worthwhile to consider the "normal" properties of these exotic Fermi liquids, which show strong anomalous temperature dependencies in various quantities like the specific heat or the BIS spectra [7]. Moreover, a number of these systems exhibit a "coherence regime" at low temperatures [7], in which the quasiparticles are supposed to form rather well defined bands. In this connection, the interesting question arises, whether a universal band structure concept for such systems exists, which combines common

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Numerical renormalization group calculations for the self-energy of the impurity Anderson model

Cited by 297 publications

References 28 publications

Finite-temperature numerical renormalization group study of the Mott transition

Finite-temperature numerical renormalization group study of the Mott transition

Numerical Renormalization Group Analysis of Interacting Quantum Dots

Quasiparticles in transition metals with strong local correlations: band formation and collective effects

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