Comment on: Locally self-consistent embedding approach for disordered electronic systems

• Published in: arXiv.org 2020-01
• Main Authors: Rostam Moradian, Moradian, Sina, Gholami, Rouhollah
• Format: Article
• Language: English
• Subjects: Alloy systems; Approximation; Dependence; Electronic systems; Electrons; Embedded systems; Embedding; Lattice sites; Localization; Mathematical analysis; Substitutes
• ISSN: 2331-8422

We comment on article by Yi Zhang , Hanna Terletska, Ka-Ming Tam, Yang Wang, Markus Eisenbach, Liviu Chioncel, and Mark Jarrell [Phys. Rev. B {\bf 100}, 054205 (2019)]\cite{Zhang} in which to study substitution disordered systems, they presented an embedding scheme for the locally self-consistent method. Here we show that their methods is a truncated case of our super-cell approximation, achieved by neglecting super-cell wave vectors dependence on self-energy \(\Sigma_{sc}({\bf K}_{n},E)\) and replacing them by a local on-site self-energy, \(\Sigma_{sc}({\bf K}_{n},E)=\Sigma_{sc}(L,L,E)\) in our articles\cite{Moradian01, Moradian02, Moradian03}. Also their real and k-space self-energies in the limit of the number of super-cell sites, \(N_{c}\), approaching the number of lattice sites, N, do not recover exact self-energies \(\Sigma(l, l', E)\) and \(\Sigma({\bf k}, E)\). For highlighting advantages of our methods with respect to other approximations such as dynamical cluster approximation (DCA)\cite{Jarrell} in capturing electron localization, we apply our real space super-cell approximation (SCA), and super-cell local self-energy approximation (SCLSA) to one and two dimensional substitution disorder alloy systems. Our electron localization probability calculations for these systems determine non zero values that indicate electrons localization.