Natural Orbital-Based Lanczos Method for Anderson Impurity Models

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. H\"{o}ppner, O. Gunnarsson, and M. W. Haverkort, Phys. Rev. B {\bf 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.