gif files of Fourrier representation with golden permutation of eigenstates 
are of the form: 
gfourier_gvec_twop_arnoldi_(...)_fig.gif

with 9 or 10 numbers in (...) representing:

1) 01 for boson case or 00 for fermion case
2) index with ordering for max \xi_E
3) initial index of Arnoldi diagonalization (not important)
4) Energie eigenvalue
5) \xi_x
6) system size N
7) interaction strength U
8) interaction range U_R
9) interaction decay parameter w if U_R>2
10) lambda parameter (position 9 if U_R=1)


======= File name structure of data files ==================
names of data files for eigenvectors are of the form:
gen_select_green_arnoldi_(...)_fib.dat

with 5-6 numbers in (...) representing:

1) 1 for boson case or 0 for fermion case
2)-5) or 6) same as 6)-9) or 10) in files name of eigenvector gif files above

======= Content of data files ===============================
the data files contain 7 columns with:
1) index with ordering for max \xi_E
2) initial index of Arnoldi diagonalization (not important)
3) Energie eigenvalue
4) \xi_E
5) \xi_x
==================
6) eigenvector error estimate obtained from: 

$\delta^2E=\delta^2\gamma/\gamma^2$ 

with $\gamma$ being the eigenvalue of the resolvent $G=1/(E-H)$ and with 
the gamma error given by:

$\delta^2\gamma=<\!\psi|\,(G-\gamma)^2\,|\psi\!>
=\|G\psi-\gamma\psi\|^2=|b|^2\,|u_{n_A}|^2$

where \psi is the (approximate) eigenvector of G (and H). 
The quantity $b$ is the last corner element in the Arnoldi decomposition which 
couples to the first outside vector $\zeta_{n_A+1}$ and which is 
normally neglected and u_{n_A} is the last component of the 
small eigenvector of the Arnoldi representation matrix which is used 
to compute \psi. The above formula is quite standard in the mathematical 
literature of the Arnoldi method (see for example Ref. [24], top of 
page 341).
Note that the column "6" describes (only) the systematic mathematical 
error of the Arnoldi method due the fact that the last coupling element 
is neglected, i. e. the cutoff of the Krylov space but it does not 
take into account certain rounding errors of other computations. 
A value of "0" for this column in the data files indicate a value below 
10^{-300} which is possible if the small Arnoldi eigenvectors u_j show strong 
localization and are computed with high precision also for the localized tails.
Data where the column 6 is >10^{-8} were removed due to bad quality 
(typically a certain fraction \sim 1/3 or less of bad quality 
Arnoldi eigenvectors has to be removed).
Values below 10^{-28} indicate that there is no systematic mathematical 
error of the Arnoldi method (i.e. virtual exact eigenvectors) and all errors 
are only due to rounding errors. 

==================
7) eigenvector error given by formula (6) using direct matrix vector 
   product and giving INDEPENDANT confirmation of quality of eigenvector
   a value of -10 (for the cases of small delocalization with \xi_E<N/100) 
   indicates that this quantity and also \xi_x were not computed and 
   \xi_x is estimated as 3*\xi_E in this file

   This error takes all errors into account, systematic Arnoldi method error 
   but also all type of rounding errors in the different computations. 
   See also short discussion below Eq. (6) of paper. 
