[Wien] Hartree-Fock and the Hubbard Model

[Karel Vyborny]

Dear Pablo,
experts in strongly correlated systems may correct me but my understanding 
is that Hubbard U is not a "model" of Hartree Fock exchange. HF is an 
approximative treatment of electron-electron interaction, a many body 
problem. Hubbard model (where U was originally introduced) tries to 
_model_ the same.

In other words, both Hubbard U and DMFT are attempts to capture the effect 
of electron correlations which are beyond HF.

Best regards,

Karel



--- x ---
dr. Karel Vyborny
Fyzikalni ustav AV CR, v.v.i.
Cukrovarnicka 10
Praha 6, CZ-16253
tel: +420220318459


On Wed, 16 Nov 2016, delamora wrote:

> 
> Dear Fabien Tran and Karel Vyborny,
> 
> Thanks for your comments.
> 
> 
> What I want to know is if the Hartree Fock exchange is what the Hubbard U is
> trying to model
> 
> What I know is that for strong intraatomic repulsion, 3d and 4f, the Hubbard
> U gives good results, although the U is a parameter.
> 
> But for intermediate intraatomic repulsion, 4d, 5d, 5f then more expensive
> methods are needed, such as DMFT
> 
> So, if this is the case that the Hartree Fock exchange is what the Hubbard U
> is trying to model then the hybrid functionals would do a better job.
> 
> So, my question is; What are the Hubbard U and DMFT trying to model?
> 
> 
> Cheers
> 
>           Pablo de la Mora
> 
> ____________________________________________________________________________
> De: Wien <wien-bounces at zeus.theochem.tuwien.ac.at> en nombre de delamora
> <delamora at unam.mx>
> Enviado: martes, 25 de octubre de 2016 11:05:08 a. m.
> Para: A Mailing list for WIEN2k users
> Asunto: Re: [Wien] Hartree-Fock and the Hubbard Model  
> Este remitente no superó nuestras comprobaciones de detección de fraude y e
> s posible que no sea quien parece ser. Obtenga información acerca de la sup
> lantación de identidad.
> Comentarios
> 
> Dear F Tran,
> 
> Thank you for your suggestion.
> 
> I found another one
> 
> http://www.wien2k.at/events/ws2015/Tran-talk_xc.pdf
> 
> It could be interesting, ja, ja (spanish accent)
> 
> I have not read them yet
> 
> 
> Saludos
> 
> 
>               Pablo
> 
> ____________________________________________________________________________
> De: Wien <wien-bounces at zeus.theochem.tuwien.ac.at> en nombre de
> tran at theochem.tuwien.ac.at <tran at theochem.tuwien.ac.at>
> Enviado: martes, 25 de octubre de 2016 02:25:25 a. m.
> Para: A Mailing list for WIEN2k users
> Asunto: Re: [Wien] Hartree-Fock and the Hubbard Model  
> Hi,
> 
> all these methods are somehow based on the Hartree-Fock method,
> which is (partially) free of self-interaction error.
> The SIE with LDA/GGA is particularly large for localized d or f
> electrons, such that LDA/GGA don't work well with these systems.
> 
> The onsite LDA+U and onsite hybrid are by far much cheaper than
> the full hybrids.
> 
> This is a good paper to read:
> http://journals.aps.org/prb/abstract/10.1103/PhysRevB.79.035103
> 
> F. Tran
> 
> On Tuesday 2016-10-25 02:09, delamora wrote:
> 
> >Date: Tue, 25 Oct 2016 02:09:24
> >From: delamora <delamora at unam.mx>
> >Reply-To: A Mailing list for WIEN2k users <wien at zeus.theochem.tuwien.ac.at>
> >To: A Mailing list for WIEN2k users <wien at zeus.theochem.tuwien.ac.at>
> >Subject: [Wien] Hartree-Fock and the Hubbard Model
> >
> >
> >Dear WIEN2k community,
> >
> >From what I understand the Hubbard Model is to calculate the electronic
> >repulsion inside the orbitals, specially in the 3d and 4f.
> >
> >Is it an approximation for the Hartree Fock exchange?
> >
> >If this is the case then it can be better calculated exact-exchange
> >functionals (1, 2)
> >
> >1) 4.5.7 Onsite-exact-exchange and hybrid functionals for correlated
> >electrons
> >
> >2) 4.5.8 Unscreened and screened hybrid functionals
> >
> >Cheers
> >
> >          Pablo de la Mora
> >
> >
> >
> 
>