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

Abstract

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

Exact equilibrium results in the interacting resonant level model

“…Contrasting this to the small (negative) U case where the hybridisation is relevant, the resonance has a finite width, and there are no discontinuities in the occupation as a function of ε 0 , we see that at some finite U < 0, there must be a quantum phase transition between the two states of the system. 3,38 This is in complete agreement with our earlier bosonization analysis, Eq. (64).…”

“…This includes the case N = 2 which is particularly important for the study of transport properties, [1][2][3]5,6,[8][9][10][11] but it is also instructive to study the model for generic N . 18,38 By making a Fourier transform with respect to chain index…”

“…Non-interacting case: substituting α = 2 into Eq. (38) gives us the relationship T B = 2T K so x = ε 0 /2T K , which can then be inserted into the non-interacting expression Eq. ( 4) and differentiated to get the standard Lorenzian form of the susceptibility…”

“…Strong coupling case: substituting α = 1 into Eq. (38) gives us the relationship T B = πT K /2 so x = 2ε 0 /πT K .…”

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

“…Introduction -Since the times of Kondo [1] and Anderson [2], physicists have been fascinated by the possible effects of embedding a correlated quantum impurity in a metallic host [3][4][5][6]. Recently, a lot of work in this area has also concentrated around the Interacting Resonant Level model (IRLM) [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]; first introduced in 1978 [7] as formally equivalent to the anisotropic Kondo model, it gained a lot of interest in its own right since various exact solutions out of equilibrium were proposed for it [13][14][15]. Despite a lot of progress being made on non-equilibrium transport in the IRLM [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], there remains open questions about equilibrium properties.…”