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

Abstract

The non-crossing approximation (NCA) is generalized for the Anderson model with finite Coulomb repulsion U . Resummation of infinite number of terms is performed so as to incorporate all leading contributions in the limit of large degeneracy of the local states. With negligible weight of the doubly occupied local states in equilibrium, the extension is achieved through simple modifications of the lowest order formulae. The single-particle excitation spectrum is calculated with almost the same computational effort as in the original NCA. The present scheme reproduces the scaling behavior of the Kondo resonance in the density of states, and gives reasonable description of thermodynamics of the finite-U Anderson model over a wide range of temperature.

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

“…It is important to take account of the SOI and CFS effects in 4f systems. 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.…”

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.…”

Exact Green's function for a multiorbital Anderson impurity at high bias voltages

“…For instance, the Wilson numerical renormalization group (NRG), 13 the density matrix renormalization group, 14 the continuous-time quantum Monte Carlo methods 15,16 and the Matsubara-voltage approach, 17 can be applied to the multi-orbital Anderson model for quantum dots in the case where the internal degrees of freedom N are not so large. Alternatively, perturbative large N approaches, such as the non-crossing approximation (NCA) [18][19][20][21][22] and 1/(N − 1) expansion 23,24 can explore the parameter regions complementary to the numerical ones.…”

“…[18][19][20][21] This method is known to give physically reasonable result at energy scales near the Kondo temperature. To work in this approximation, we rewrite the Hamiltonian, given by Eqs.…”