Functional renormalization group study of the interacting resonant level model in and out of equilibrium

Physical Review B - Condensed Matter and Materials Physics

Volumn 81, Issue 12, 2010, Pages

  Karrasch, C ^a   Pletyukhov, M ^a   Borda, L ^b,c   Meden, V ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b UNIVERSITY OF BONN   (Germany)

^c BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77953209568     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.125122     Document Type: Article

References (55)

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42. The shortcoming of the "reservoir-cutoff" scheme introduced in Ref. is that when implemented within the Matsubara formalism, second-order results are quantitatively inferior to those of the Θ -function approach. Namely, if one discards the flow of the three-particle vertex γ 3 Λ but fully accounts for the frequency-dependence of γ 2 Λ, the former (the latter) gives reasonable results for the single impurity Anderson model in comparison with NRG data up U / Γ = 2 (U / Γ = 6), respectively (see Ref.). In order to tackle larger values of U within the reservoir-cut-off approach, the second-order flow equations have to be further approximated (by neglecting, e.g., certain frequency-dependencies or self-energy feedbacks). For the problem at hand, we briefly present equilibrium second-order FRG results obtained from the sharp cut-off scheme only (see the Appendix).
43. Similarly, one can show that in case of structureless leads implementing the reservoir cut-off scheme of Sec. directly within the Matsubara formalism gives the same analytic approximate (i.e., truncated to first order) self-energy flow equation as obtained using the sharp cut-off procedure.
44. ′ is finite (Ref.).
45. In this case, we use the reservoir cut-off scheme only which allows for a simple interpretation of the self-energy as effective system parameters. Physical quantities (and the question whether they are governed by power laws in the scaling limit) will be investigated numerically using both nonequilibrium FRG frameworks (see Sec.).
46. In case of the single-channel IRLM, T K can be related to the Kondo temperature of the anisotropic Kondo model (Refs.).
47. Standard NRG is a well-established numerical tool to compute low-energy equilibrium properties of quantum impurity systems. A detailed introduction to this method can be found in Ref..
48. For the single-channel IRLM, the same equilibrium exponent (which to leading order in U agrees with α χ) was computed from the functional and numerical renormalization group frameworks as well as by mapping the system to the anisotropic Kondo model by virtue of bosonization (Ref.). As for the two-channel case, the simple FRG approximation scheme employed in this paper agrees with the other approaches up to fairly large Coulomb interactions.
49. The equilibrium low energy scale T K can actually be defined as the voltage regime where the current crosses from a linear increase to a power-law decay (by considering, e.g., the maximum value of J). Except for prefactors, this definition is as expected equivalent to the one of Eq., at least within the FRG approximation.
50. res evolves beyond the linear regime.
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