Band Calculation for Ce-Compounds on the basis of Dynamical Mean Field Theory

Abstract

The band calculation scheme for f electron compounds is developed on the basis of the dynamical mean field theory (DMFT) and the LMTO method. The auxiliary impurity problem is solved by a method named as NCAf 2 v', which includes the correct exchange process of the f 1 → f 2 virtual excitation as the vertex correction to the non-crossing approximation (NCA) for the f 1 → f 0 fluctuation. This method leads to the correct magnitude of the Kondo temperature, T K , and makes it possible to carry out quantitative DMFT calculation including the crystalline field (CF) and the spin-orbit (SO) splitting of the self-energy. The magnetic excitation spectra are also calculated to estimate T K . It is applied to Ce metal and CeSb at T = 300 K as the first step. In Ce metal, the hybridization intensity (HI) just below the Fermi energy is reduced in the DMFT band. The photo-emission spectra (PES) have a conspicuous SO side peak, similar to that of experiments. T K is estimated to be about 70 K in γ-Ce, while to be about 1700 K in α-Ce. In CeSb, the double-peak-like structure of PES is reproduced. In addition, T K which is not so low is obtained because HI is enhanced just at the Fermi energy in the DMFT band. lation of DES of the auxiliary impurity Anderson model in an effective medium. 3 At present, however, we do not have the theoretical method which analytically gives correct DES of the impurity Anderson model. Several numerical methods have been developed to calculate DES of the Kondo problem. It is known that the quantum Monte Carlo (QMC) method 7, 8 and the numerical renormalization group (NRG) method 9 give in principle correct DES. They are applied to DMFT calculation, 8, 10 but they have difficulties in application to the realistic band calculation of f electron systems. 6,11 Approximate but highly flexible approaches have been developed on the basis of the resolvent technique. 12 The NCA method 13, 14 has been widely applied to various models though it has some weakness in application at very low temperatures: it does not fulfill the Fermi liquid relation. But it can be easily applied to realistic situations such as the competition between the Kondo effect and the crystalline field (CF) splitting. 14 NCA has been also applied to the DMFT calculation. 15 The NCA equation is justified by the 1/N f expansion when the fluctuation of the valence is restricted to the f 1 and f 0 configurations, where N f is the degeneracy factor of the f orbital. 14 However, the exchange coupling through the virtual excitation to the f 2 configuration is not negligible in quantitative calculation. A scheme which includes the f 2 configuration in the frame work of the NCA type diagram has been used. However, it does not lead to the Kondo temperature (T K ) given by using the exchange constant obtained by the Schrieffer-Wolff (S-W) transformation. 16 Therefore, the exchange process through the f 2 configuration is not properly accounted in the scheme. Actually, the DMFT calculation by using this method gives a too small Kondo resonance peak c...

Band Calculations for Ce Compounds with AuCu3-Type Crystal Structure on the Basis of Dynamical Mean Field Theory: II. CeIn3 and CeSn3

“…A theory named NCAf 2 vc (noncrossing approximation including the f 2 state as a vertex correction) has been developed [14][15][16] and combined with the linear muffintin orbital (LMTO) method to carry out the DMFT band calculation. 16,17) NCAf 2 vc can include CFS and the SOI effect and also the correct exchange process of the f 1 → f 0 , f 2 virtual excitation. The calculation gives an accurate order of the Kondo temperature (T K ).…”

Conserving approximations in direct perturbation theory: new semianalytical impurity solvers and their application to general lattice problems

“…Both of these approximations involve time-consuming numerical calculations; up to now a generalization to the even more demanding case of finite U-values has not been reported. Other approximation schemes involving additional simplifying assumptions for the ionic propagators and vertex functions, be it either in a non-conserving [47] or conserving fashion [48], will not be considered here. Although they may be useful with respect to computational effort, they have only been justified for the case of large orbital degeneracy.…”

Extension of the Non-Crossing Approximation for the Anderson Model with Finite Coulomb Repulsion

“…2 v scheme Before we present formulations for the single-particle excitation, we summarize the NCAf 2 v scheme developed by Sakai et al 4,15 In order to derive the self-energy, they have introduced the vertex part Λ(z, ǫ) which consists of the 4f…”

“…In addition to results in the present scheme, results in the other schemes are shown for comparison: (i) ρ (S) f , which considers the vertex correction in the self-energy of resolvents but not in the Green function, 4,15 (ii) NCAf 2 , which is the lowest order selfconsistent approximation including 4f 2 states but without the vertex correction, and (iii) infinite-U NCA, which is the original NCA with infinite Coulomb repulsion. Figure 5 shows single-particle excitation with parameters n = 6, W 0 = 30, ǫ f = −1200 and U = 3|ǫ f | = 3600 at temperatures T = 20 and T = 0.1.…”