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Scaling theory vs exact numerical results for spinless resonant level model

Kiss, Annamária, Junya Otsuki, Yoshio Kuramoto

Published Jan 1, 2013• 4 citations
OpenAlex

Abstract

The continuous-time quantum Monte Carlo method is applied to the interacting resonant level model (IRLM) \nusing double expansion with respect to Coulomb interaction Ufc and hybridization V . Thermodynamics of the \nIRLM without spin is equivalent to the anisotropic Kondo model in the low-energy limit. Exact dynamics and \nthermodynamics of the IRLM are derived numerically for a wide range of Ufc with a given value of V . For \nnegative Ufc, excellent agreement including a quantum critical point is found with a simple scaling formula that \ndeals with V in the lowest-order, and Ufc up to infinite order. As Ufc becomes positive and large, lower order \nscaling results deviate from exact numerical results. Possible relevance of the results is discussed to certain \nSamarium compounds with unusual heavy-fermion behavior.

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•Dec 1, 2017•1 citation
The continuous-time quantum Monte Carlo method is applied to the interacting resonant level model (IRLM) \nusing double expansion with respect to Coulomb interaction Ufc and hybridization V . Thermodynamics of the \nIRLM without spin is equivalent to the anisotropic Kondo model in the low-energy limit. Exact dynamics and \nthermodynamics of the IRLM are derived numerically for a wide range of Ufc with a given value of V . For \nnegative Ufc, excellent agreement including a quantum critical point is found with a simple scaling formula that \ndeals with V in the lowest-order, and Ufc up to infinite order. As Ufc becomes positive and large, lower order \nscaling results deviate from exact numerical results. Possible relevance of the results is discussed to certain \nSamarium compounds with unusual heavy-fermion behavior.
In this paper we develop a method to describe perturbatively the entanglement entropy in a simple impurity model, the Interacting Resonant Level Model (IRLM), at low energy (i.e. in the strong coupling regime). We use integrability results for the Kondo model to describe the infrared fixed point, conformal field theory techniques initially developed by Cardy and Calabrese and a quantization scheme that allows one to compute exactly Renyi entropies at arbitrary order in 1/TB in principle, even when the system size or the temperature is finite. We show that those universal quantities at arbitrary interaction parameter in the strong coupling regime are very well approximated by the same quantities in the free fermion system in the case of attractive Coulomb interaction, whereas a strong dependence on the interaction appears in the case of repulsive interaction.
We apply a combination of numerical renormalization group (NRG) and renormalized perturbation theory (RPT) to a model of two quantum dots (impurities) described by two Anderson impurity models hybridized to their respective baths. The dots are coupled via a direct Coulomb interaction U12{U}_{12}U12​ and a spin exchange interaction JJJ. The model has two types of quantum critical points, one at J=JcJ={J}_{c}J=Jc​ to a local singlet state and one at U12=U12c{U}_{12}={U}_{12}^{c}U12​=U12c​ to a locally charge ordered state. The renormalized parameters which determine the low energy behavior are calculated from the NRG. The results confirm the values predicted from the RPT on the approach to the critical points, which can be expressed in terms of a single energy scale T∗{T}^{*}T∗ in all cases. This includes cases without particle-hole symmetry, and cases with asymmetry between the dots, where there is also a transition at J=JcJ={J}_{c}J=Jc​. The results give a comprehensive quantitative picture of the behavior of the model in the low energy Fermi liquid regimes, and some of the conclusions regarding the emergence of a single energy scale may apply to a more general class of quantum critical points, such as those observed in some heavy fermion systems.
We study a spinless level that hybridizes with a fermionic band and is also coupled via its charge to a dissipative bosonic bath. We consider the general case of a power-law hybridization function $\ensuremath{\Gamma}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}}^{r}$, with $r\ensuremath{\geqslant}0$, and a bosonic-bath spectral function $B(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{s}$, with $s\ensuremath{\geqslant}\ensuremath{-}1$. For r<1r<1r<1 and $\mathrm{max}(0,2r\ensuremath{-}1)<s<1$, this Bose-Fermi quantum impurity model features a continuous zero-temperature transition between a delocalized phase, with tunneling between the impurity level and the band, and a localized phase, in which dissipation suppresses tunneling in the low-energy limit. The phase diagram and the critical behavior of the model are elucidated using perturbative and numerical renormalization-group techniques, between which there is excellent agreement in the appropriate regimes. For r=0r=0r=0, this model's critical properties coincide with those of the spin-boson and Ising Bose-Fermi Kondo models, as expected from bosonization.
We study the effect of screening of an impurity charge by conduction electrons on resonant tunneling at arbitrary energy of the impurity level. We examine the exactly solvable model of the resonant level. We find the ground-state solutions of the model at all possible Coulomb interactions. The principle of equivalence between its universal behavior and the Kondo model is proved. However, the dependence of its scale invariant variable on the bare variables has different forms in two different regions of the parameter variations. This means that besides the well-known Kondo-like fixed point of the renormalization at weak Coulomb interaction a new stable point exists. The latter determines a singular low-energy behavior of the impurity. Based on the solution, the tunneling amplitude is calculated. It is shown that for a narrow gap or quasi-one-dimensional junction a severe renormalization of the one-electron half-width ${\mathrm{\ensuremath{\Gamma}}}_{0}$ occurs ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{R}}$\ensuremath{\propto}${\mathrm{\ensuremath{\Gamma}}}_{0}$(${\mathrm{\ensuremath{\Gamma}}}_{0}$/D${)}^{\mathrm{\ensuremath{\alpha}}/(1\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}})}$. The comparison with perturbation results is discussed. Finally the conductance of the junction with randomly located impurities is calculated to clarify the crucial role of the non-Fermi-liquid behavior on the resonant tunneling under certain conditions.
We reinvestigate the large degeneracy solution of the multichannel Kondo problem, and show how in the universal regime the complicated integral equations simplifying the problem can be mapped onto a first-order differential equation. This leads to an explicit expression for the full zero-temperature scaling functions at---and away from---the intermediate non-Fermi-liquid fixed point, providing complete analytic information on the universal low---and intermediate---energy properties of the model. These results also apply to the widely used noncrossing approximation of the Anderson model, taken in the Kondo regime. An extension of this formalism for studying finite-temperature effects is also proposed and offers a simple approach to solve models of strongly correlated electrons with relevance to the physics of heavy fermion compounds.