[Pw_forum] why are there two Fermi energies?

Eduardo Ariel Menendez Proupin eariel99 at gmail.com
Thu Apr 21 15:01:31 CEST 2011

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.

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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