Double-counting correction for correlated electrons

Introduction

Correcting the hamiltonian for correlated electrons ( as for d or f electrons) faces the problem of the double counting because these correlated electrons are yet included in the main hamiltonian.

Since the tratement of the correlated electrons is done by the division of the system into 2 subsystems: one subsystem for non-correlated electrons treated by the classical main hamiltonian, another subsystem for the correlated electrons.

The idea is to substract the latter electrons from the main hamiltonian otherwise we will face the double counting problem.

How to substarct the correlated electrons from the main hamiltonian?

There many ways to do that. We present some of them:

1- Methods for DFT+U approach

 - Self-Interaction Correction SIC introduced by Anisimov et al. 1993, with an approximate correction for the self-interaction correction. This is probably best suited for strongly correlated systems and for a full potential method we recommend to use an “effective” Uef f = U − J; setting J = 0.

- Around the Mean Field AMF  introduced by Czyzyk and Sawatzky (1994 ) as ’Around the Mean Field’ method. (In Novak et al. 2001 it is denoted as LDA+U(DFT)). This version is (probably) ´ more suitable for metallic or less strongly correlated systems.

- Hubbard model in the mean field approximation HMF introduced by Anisimov et al. ( 1991 ) is also implemented. Note, however, that it is to be used with the LDA (not LSDA) exchange-correlation potential in spin polarized calculations!

- Full localized limit FLL introduced by  A. Lichtenstein et al (1995 ) 

References:

http://www.abinit.org/doc/helpfiles/for-v7.8/tutorial/lesson_ldau.html

http://elk.sourceforge.net/CECAM/Nordstrom-DFT+U.pdf

http://yclept.ucdavis.edu/Theses/Erik.thesis.pdf

http://scs.sa.infn.it/TCXIV/Download/Anisimov/Salerno-1-asus.pdf

http://pitp.physics.ubc.ca/confs/sherbrooke/archives/pitpcifar_sherbrooke2008_dft_u_cote.pdf

http://yclept.ucdavis.edu/Publ/EECE.publ.pdf


2- Methods for DFT+DMFT approach

- Around the Mean Field AMF

- Fully localized limit FLL

References:

http://www.cond-mat.de/events/correl14/manuscripts/wehling.pdf

http://www.physics.rutgers.edu/~haule/papers/ExactDC.pdf

https://arxiv.org/pdf/1110.2782.pdf

http://physics.stackexchange.com/questions/51785/double-counting-correction-in-a-lda-dmft-calculation

https://arxiv.org/abs/1004.4569

http://e-collection.library.ethz.ch/eserv/eth:48594/eth-48594-02.pdf

http://www.chrismarianetti.org/static/publications/1409.4135v1.pdf