Numerical renormalization group study of the Anderson-Holstein impurity model

Abstract

We present numerical renormalization group (NRG) calculations for a single-impurity Anderson model with a linear coupling to a local phonon mode. We calculate dynamical response functions, spectral densities, dynamic charge and spin susceptibilities. Being non-perturbative, the NRG is applicable for all parameter regimes. Our calculations cover both weak and strong electron-phonon coupling for zero and finite electron-electron interaction. We interpret the high-and low-energy features and compare our results to atomic limit calculations and perturbation theory. In certain restricted parameter regimes for strong electron-phonon coupling, a soft phonon mode develops inducing a very narrow resonance at the Fermi level.

Effects of electron-phonon coupling in the Kondo regime of a two-orbital molecule

“…[39][40][41][42][43][44][45][46][47][48][49][50][51] It is well-established for this model that the ratio ω 0 /Γ is a key quantity governing the interplay between e-ph interactions and the Kondo effect. In the instantaneous or anti-adiabatic regime ω 0 ≫ Γ, the bosons adjust rapidly to any change in the orbital occupancy, leading to polaronic shifts in the orbital energy and in the Coulomb interaction and to exponential suppression of certain virtual tunneling processes.…”

“…46 The effective conduction band formed by the even-parity combination of left-and right-lead electrons is divided into logarithmic bins spanning the energy ranges DΛ −(m+1) < ±ε < DΛ −m for m = 1, 2, 3, . .…”

“…31 For example, the essential physics of certain experiments 24,26 appears to be described by variants of the Anderson-Holstein model, which augments the Anderson model 37 for a magnetic impurity in a metallic host with a Holstein coupling 38 of the impurity charge to a local phonon mode. Variants of the model have been studied since the 1970s in connection with other problems [39][40][41][42][43][44][45][46][47][48][49] prior to their application to singlemolecule devices. [50][51][52][53][54][55][56][57][58][59] Various analytical approximations as well as nonperturbative numerical renormalization-group calculations have shown that in equilibrium, the Holstein coupling reduces the Coulomb repulsion between two electrons in the impurity level, even yielding effective e-e attraction for sufficiently strong e-ph coupling.…”

Slave boson theory for transport through magnetic molecules with vibronic states

“…As the Coulomb charging energies in these systems can be considerably reduced by screening due to the electrodes, 14 electronic and vibrational energies can become of the same order of magnitude generating scenarios where novel effects may emerge. 15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32 The effect of the coupling between electronic excitations and vibronic states in molecular transistors depends on the symmetry and frequency of the vibrating mode and on the strength of the coupling. Symmetric modes with a Holstein coupling between quantized vibrations and electronic levels may strongly renormalize the molecular parameters reducing charging energies 15 and producing anomalous behavior of the Kondo temperature versus applied gate voltages.…”

Slave-boson approach to the infinite-UAnderson-Holstein impurity model

“…8 Recently, the HH model was studied with DMFT in combination with the numerical renormalization group (NRG) at half-filling at zero temperature. 4,9 The NRG method has also been successfully applied to AH model 6,7 , and almost exact results on the electron and phonon spectral functions have been obtained. However, it is still desirable to develop an analytic scheme in spite of its approximate nature since it helps us to understand the underlying physics in more clear and intuitive way.…”