Output Files

Once the analytic continuation simulation is finished, the final spectral function $A(\omega)$ is outputted to Aout.data. Note that $A(\omega)$ is equivalent to the imaginary part of real frequency Green's function Im$G(\omega)$. Then the ACFlow toolkit will automatically calculate the corresponding real part Re$G(\omega)$ via the Kramers-Kronig transformation. The full Green's function at real axis $G(\omega)$ is stored in Gout.data. The spectral function is also used to reconstruct the imaginary time or Matsubara Green's functions [$\tilde{G}(\tau)$ or $\tilde{G}(i\omega_n)$], which is stored in repr.data. Besides the three output files, the ACFlow toolkit will generate quite a few output files, which can be used to analyze and diagnose the calculated results. All of the possible output files of the ACFlow toolkit are collected and explained in Table 1.

Filename	Description
`Aout.data`	Final spectral function $A(\omega)$.
`Aout.data.alpha`_$i$	$\alpha$-resolved spectral function $A_{\alpha}(\omega)$ for the `StochAC` solver.
`repr.data`	Reproduced Green's function $\tilde{G}$ at imaginary time or frequency axis.
`Gout.data`	Full Green's function at real axis $G(\omega)$.
`chi2.data`	$\log_{10}(\chi^2)$ vs $\log_{10}(\alpha)$.
`goodness.dat`	$\log_{10}(\chi^2)$ vs $\log_{10}(\Theta)$ for the `StochSK` solver.
`model.data`	Default model $m(\omega)$.
`prony.data`	Prony approximation to the Matsubara data (for the `BarRat` solver).
`Gprony.data`	Preprocessed Matsubara data by Prony approximation (for the `BarRat` solver).
`barycentric.data`	Barycentric rational function approximation to the Matsubara data (for the `BarRat` solver)
`hamil.data`	$U(\alpha)$ vs $\alpha$ for the `StochAC` solver.
`passed.data`	Indices of selected solutions for the `StochOM` and the `StochPX` solvers.
`pole.data`	Amplitudes and positions of the poles for the `StochPX` solver.
`prob.data`	$P[\alpha\|\bar{G}]$ vs $\alpha$ for the `MaxEnt` solver (`bryan` algorithm).
`stat.data`	Monte Carlo statistical information for stochastic sampling methods.
`err.out`	Error or exception messages (stacktrace) collected during simulation.

Table 1 | Possible output files of the ACFlow toolkit.

Warning

For bosonic systems, the MaxEnt, StochAC, StochSK, and StochOM solvers will generate and output $\tilde{A}(\omega)$, instead of traditional $A(\omega)$. That is to say, in Aout.data, the data are actually $\tilde{A}(\omega)$. If the users want to retrieve $A(\omega)$, they have to do the transformation by themselves:

\[\tilde{A}(\omega) = \frac{A(\omega)}{\omega},\]

or resort to Gout.data. On the other hand, the BarRat and StochPX solvers will always generate and output $A(\omega)$, irrespective of bosonic and fermionic systems.

The NevanAC solver doesn't support bosonic system directly.