Natural orbital-based Lanczos method for Anderson impurity models

Abstract

We implement the Lanczos algorithm on natural orbital basis to solve the zero-temperature Green's function of Anderson impurity models, following the work of Y. Lu, M. Höppner, O.Gunnarsson, and M. W. Haverkort, Phys. Rev. B 90 (2014) 085102. We present the technical details, generalize the algorithm to the cases of particle-hole asymmetry, with local magnetic field, and of two impurities. The results are benchmarked with conventional Lanczos, quantum Monte Carlo, and numerical renormalization group methods, demonstrating its potential as a powerful impurity solver for the dynamical mean-field theory.Keywords: Lanczos, natural orbital, Anderson impurity model, quantum impurity solver IntroductionThe Anderson impurity model (AIM) [1] is one of the basic models in condensed matter physics. It describes the physics of a local electron orbital with on-site Coulomb repulsion embedded in a conduction electron band and is widely used to describe the dilute magnetic impurities in metals [2], Kondo effect [3], as well as impurity quantum phase transitions [4]. In the past two decades, stimulated by the development and application of the dynamical mean-field theory (DMFT) [5,6], the study of AIM receives revived attention because in DMFT, a lattice Hamiltonian for the correlated electrons is mapped into an AIM with self-consistently determined electron bath. The core calculation of DMFT is the iterative solution of the self-energy *