Scaling Theory vs Exact Numerical Results for Spinless Resonant Level Model

Kiss, Annamária; Otsuki, Junya; Kuramoto, Yoshio

doi:10.7566/jpsj.82.124713

Cited by 5 publications

(17 citation statements)

References 27 publications

(47 reference statements)

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“…where d = β 2 /16π is the scaling dimension of the boundary operator given in (19) above, and λ = 1 d − 1. Rearranging this, comparing with Eq.…”

Section: A Bosonizationmentioning

confidence: 99%

“…There have been a number of previous numerical studies of the IRLM with the numerical renormalization group (NRG), 2,3,18,19 and while good agreement is usually found for small interactions, there is usually a significant divergence for larger interactions. Here, we present results from both NRG and density matrix renormalization group (DMRG) where we show that there is very good agreement with Eq.…”

Section: Numerics; Nrg and Dmrgmentioning

confidence: 99%

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Exact equilibrium results in the interacting resonant level model

2019

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We present exact results for the susceptibility of the interacting resonant level model in equilibrium. Detailed simulations using both the Numerical Renormalization Group and Density Matrix Renormalization Group were performed in order to compare with closed analytical expressions. By first bosonizing the model and then utilizing the integrability of the resulting boundary sine-Gordon model, one finds an analytic expression for the relevant energy scale TK with excellent agreement to the numerical results. On the other hand, direct application of the Bethe ansatz of the interacting resonant level mode does not correctly reproduce TK -however if the bare parameters in the model are renormalised, then quantities obtained via the direct Bethe ansatz such as the occupation of the resonant level as a function of the local chemical potential do match the numerical results. The case of one lead is studied in the most detail, with many results also extending to multiple leads, although there still remain open questions in this case. arXiv:1810.08246v2 [cond-mat.str-el]

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“…where d = β 2 /16π is the scaling dimension of the boundary operator given in (19) above, and λ = 1 d − 1. Rearranging this, comparing with Eq.…”

Section: A Bosonizationmentioning

confidence: 99%

Section: Numerics; Nrg and Dmrgmentioning

confidence: 99%

Exact equilibrium results in the interacting resonant level model

2019

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“…Here, we follow a different way. Namely, we extend the method that we used in our previous work 14) to the case of multi channels for the conduction electrons to obtain the hybridization renormalized by the Coulomb interaction. In that work we derived the effective hybridization for the single-channel case by using the effective Hamiltonian method 15) to take account of the simultaneous effect of the hybridization V and Coulomb interaction U f c .…”

Section: Scaling Energy With Multiple Conduction Channelsmentioning

confidence: 99%

“…In this section, we analyze the MIRLM using the continuous-time quantum Monte Carlo method. 19) In the previous paper, 14) we presented an algorithm for the single-channel case, M = 1, based on an expansion with respect to V and U f c . The advantage of the double-expansion algorithm compared with an ordinary weak-coupling expansion with respect to U f c is that the computational cost increases only linearly as M is increased, yielding efficient calculations for large M .…”

Section: Continuous-time Quantum Monte Carlo Approachmentioning

confidence: 99%

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Exact Dynamics of Charge Fluctuations in the Multichannel Interacting Resonant Level Model

2015

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A modified version of the spinless Anderson model is studied by means of the continuoustime quantum Monte Carlo method. This study is motivated by the peculiar heavy-fermion behavior observed in certain Samarium compounds, which is insensitive to magnetic field. The model involves M channels for conduction electrons, all of which interact with local f electron via the Coulomb repulsion U f c , while only one channel has hybridization with the local state. The effective hybridization is reduced by the Anderson orthogonality effect, and a quantum critical point occurs with increasing M and/or increasing U f c . The numerical results at finite temperature of the local charge susceptibility are well fitted by a simple scaling theory for all M . However, the single-particle spectrum is described by a double Lorentzian for M > 1, in contrast with the single Lorentzian with M = 1. A quasi-particle perturbation theory is presented that reproduces the quantum critical point for large M . The quasi-particle theory gives not only the renormalized energy scale, but its extrapolation toward higher energies being consistent with the double Lorentzian spectrum.KEYWORDS: charge Kondo effect, continuous-time quantum Monte Carlo method, quasi-particle perturbation theory, thermodynamic and dynamic properties IntroductionRecently, peculiar heavy-fermion behavior has attracted attention in certain Samarium compounds with large specific heat coefficient γ which is insensitive to external magnetic field. For example, the filled skutterudite compound SmOs 4 Sb 12 has γ ∼ 0.8J/(K 2 · mol) even though it is mixed valent. 1) Similar behavior has been found in systems such as SmPt 4 Ge 12 2) and SmT 2 Al 20 with T=Ti,V,Cr,Ta. 3-5) The resistivity of SmT 2 Al 20 shows clear Kondo-like logarithmic temperature dependence, which however is insensitive to external magnetic field.3) It has been suspected that charge degrees of freedom is responsible for the heavy mass because of the field-insensitivity, in striking contrast to ordinary Kondo effect which is sensitive to magnetic field.Motivated by these experimental observations we search for a charge fluctuation mechanism that gives rise to energy scale much smaller than bare hybridization. As the simplest attempt, we study the (spinless) multichannel interacting resonant level model (MIRLM) by means of the continuous-time quantum Monte Carlo method, which starts from the Anderson model involving the hybridization (V ) of the local charge with only one of the conduction electron orbitals, but includes additional Coulomb interaction (U f c ) felt by all conduction orbitals with the local f state. The Hamiltonian of this model is written as

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Local density of states of the interacting resonant level model at zero temperature

2022

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We present results of the impurity local density of states of the interacting resonant level model at zero temperature. We concentrate on low-energy properties and predominantly use the numerical renormalisation group technique. As interaction is increased, we find that the resonance peak at zero energy disappears, while two new peaks at finite energy emerge. This is in the absence of any field breaking the resonance. We further show that the height of the spectral function does not scale in the same way as the width, and in fact defines a second distinct exponent. We back up our results with analytic strong-coupling calculations as well as an analytic diagrammatic renormalisation group calculation that rather surprisingly gets the second exponent exactly, even for strong interactions.

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Scaling Theory vs Exact Numerical Results for Spinless Resonant Level Model

Cited by 5 publications

References 27 publications

Exact equilibrium results in the interacting resonant level model

Exact equilibrium results in the interacting resonant level model

Exact Dynamics of Charge Fluctuations in the Multichannel Interacting Resonant Level Model

Local density of states of the interacting resonant level model at zero temperature

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