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eta issue answer based on Arjan comment

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Pierre-Francois Loos 2019-12-09 10:09:03 +01:00
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Response_Letter/Response_Letter.tex
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@ -90,11 +90,17 @@ We look forward to hearing from you.
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{In Section III the authors mention that the infinitesimal eta is put to 0. {In Section III the authors mention that the infinitesimal eta is put to 0.
This is physically incorrect. This is physically incorrect.
eta is a positive infinitesimal and cannot be just put to zero. Numerically it has been shown that indeed the self energy becomes discontinuous by doing so. eta is a positive infinitesimal and cannot be just put to zero.
Numerically it has been shown that indeed the self energy becomes discontinuous by doing so.
This is the main reason for the low quality rating. } This is the main reason for the low quality rating. }
\\ \\
\alert{Titou: I don't agree with this.} \alert{Physically, $\eta$ ensures the correct time ordering when passing from $(t-t')$ to $\omega$ by a Fourier transform.
It is an infinitesimal which should be put to zero at the very end of the calculation.
In practice, this is not possible as one would have to solve everything analytically.
Therefore, one has to make a choice: set it equal to zero from the start or set it equal to a small value.
So physically, one could say that both are equally correct (or equally incorrect).
As a numerical check, we have performed additional calculations with very small $\eta$ values and the corresponding quasiparticle energies are nearly identical.
Moreover, we do not have any numerical issues in our calculations.}
\item \item
{Figures 1, and the corresponding figures in the supplementary are plotted on a linear scale of X. {Figures 1, and the corresponding figures in the supplementary are plotted on a linear scale of X.
Personally I think it is much more instructive to plot against X$^{-3}$, which will much clearer visualize convergence. } Personally I think it is much more instructive to plot against X$^{-3}$, which will much clearer visualize convergence. }