[Pw_forum] why are there two Fermi energies?

[Alex Smogunov]

Hello

2011/4/21 Eduardo Ariel Menendez Proupin <eariel99 at gmail.com>

> Hi,
> Let me clarify that I found no difference between version 4.2.1 and others.
> I have used only 4.2.1.
>
> I suspected that the Fermi level was a way to control the occupations.
> However, using different fermi levels will produce different charge
> densities because the occupation numbers will be different. If both types of
> calculations produce the same energy, then the ground state is degenerate,
> but the one with two Fermi energies seems incompatible with thermodynamics.
> I used Fermi smearing, by the way.
>
> I am committed to teaching duties today. Thanks for your answers, and I
> will come back tomorrow, or maybe late today, and I will look at the
> occupations using verbosity = .true.
>
> Mathematically it seems logical that to control  the number of electron
> (one degree of freedom) one needs one parameter, which is the Fermi level.
> To control an additional degree of freedom, the magnetization, one needs an
> additional parameter, then it is reasonable to use two Fermi levels or an
> equivalent set of two parameters.
> For example, one could define a single Fermi level and apply a shift to the
> spin down eigenvalues. This needs a physical interpretation, as well as
> having to Fermi levels.
>

Shift in eigenvalues can be seen as produced by external magnetic fiels (a
Zeeman term) then the state with two different Fermi energies may be thought
of a true ground state with only one Fermi level but in the presence of this
stabilizing magnetic field proportional to the difference in Fermi energies.
The true ground state with equal Efs do not need of course this magnetic
field.

regards,
Alexander



>
> Moreover, reversing the reasoning, I wonder why or how one gets the same
> number of electrons and magnetization using only one parameter (Fermi level)
> in the case of not using tot_magnetization. Is it a hazard or is there a
> trick that bias the calculation to the integer magnetization?
>
> Best regards
> --
>
>
> Eduardo Menendez
> Departamento de Fisica
> Facultad de Ciencias
> Universidad de Chile
> Phone: (56)(2)9787439
> URL: http://fisica.ciencias.uchile.cl/~emenendez
>
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