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Gauge derivative - 1/2 factor and gradient flow #38

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@simone-romiti simone-romiti commented Jan 27, 2023

I may have found the reason behind the bug reported by David Albandea.
He suggested that for $SU(2)$ our derivative with respect to the gauge field in in the gradient flow evolution should be multiplied by 1.0/4.0 (i.e. replacing 2.0 with 1/2.0 in the factor in front).

This is due to the different normalization we choose for the generators of the group algebra. If we want to use the same derivative routine we use for the HMC, we need to multiply the force by 2.0*beta/N_c and also by:

  • $U(1)$ : 1.0/2.0
  • $SU(2)$: 1.0/4.0 (and the same for $SU(N)$ in general)

in order to get the correct results.
In the code this is implemented with an additional attribute of the hamiltonian field class: a double dependent by the number of colors initialized in the constructor.

todo: write a program that can merge 2 .h5
…. 14 of https://arxiv.org/pdf/hep-lat/9804008.pdf. They are the same as before, no previous result needs to be changed
… format more easily readable by hadron.

To do:
- write the documentation on why this is done separately and not in the c++ code
- change the script such that the data in the old format can be removed
- generalize the script to do the same also for the correlators
script can be used for correlators and interpolators
HighFive dependence now optional
	modified:   hadron/glueball.py
verbose output + fixed wrong index in loop (some i_j pair were not analyzed)
@simone-romiti simone-romiti mentioned this pull request Jan 30, 2023
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Please see updated pull request #44

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