Free energy

[mitsuaki1987]

Hello,

I am looking for an impurity solver which can compute the free energy.
If there is such a solver, I will make it possible that DCore calls that solver.

Best regards,
Mitsuaki Kawamura

[mitsuaki1987]

Is it difficult to compute from the logarithm of the partition function ?
Is there a numerical difficulty such as the statistical noise ?

Best regards,
Mitsuaki Kawamura

[shinaoka]

Not that simple.
Let us start with the energy, which should be easier to compute.
The energy is the sum of kinetic energy (summation over k space) and the correlation energy.
The current implementation of the computation of kinetic energy in DFTTools depends on Wien2k.
But, in principle, we can implement the same functionality in DFTTools.

The correlation energy can be computed from the Green's function and the self-energy.
I think it is already implemented in DFTTools.
This algorithm may be unstable against statistical errors since we need to integrate some quantity up to high Matsubara frequencies.
I've never tried to compute the energy. I do not have any experience.

@j-otsuki
Do you know how to compute the free energy in DMFT framework?

[j-otsuki]

@shinaoka
I have seen a literature on how to compute the free energy in (cluster-)DMFT, but forgot which reference...

@mitsuaki1987
In DMFT, normally, we access thermodynamics from the internal energy, as Shinaoka-san explained.
The free energy would be more involved, because we can directly evaluate only F_imp (the free energy in the effective impurity model). F_lat (free energy in the original lattice model) needs to be reconstructed from F_imp and something else.

[shinaoka]

There is some reference on how to compute the free energy.

https://arxiv.org/pdf/1501.06936.pdf