SUN FLEX

The following information is printed by executing the SU(N) version of the program
$[...\vert]$ flex_input_file [options]
Options:

file	Filename of the trial spectral function
-T	Temperature (0.001)
-U	Coulomb repulsion (1)
-mu	Chemical potential (0.5)
-alpha	Mixing parameter (0.2)
-alpha_mu	Mixing parameter for mu (1)
-nd	Desired doping (1)
-ph_reduce	Weather to screen PH diagrams with PP effective interaction (0)
-Na	Number of additional points around fermi function (50)
-Ns	Twice the number of bands (2)
-si	Data will be read from standard input
-max_diff	Criterium tu stop self-consistency (0.0001)
-max_steps	Criterium tu stop self-consistency (300)
-ph	Wheather to include PH-channel (1)
-pp	Wheather to include PP-channel (1)
-gw	Wheather to include GW-channel (1)
-g0	Use G or G0 (g0=1 - use G0, g0=0 - use G) (0)
-hs	Weather to fix hartree term to be proportional to the input nd (0)
-do	Debug output (prints spec. fun. every iteration) (0)

Below, some more information is given for each parameter of the program. But first, let us run the example program to illustrate how it works. In the subdirectory work a file with name history.flex is located which saves all previous command lines for easier restart of the program in the future. The last command line is already written and user can copy the command line to the shell and execute
../flx start/Aflex_N_4_U_1_nd_0.8_T_0.001_pp_ph_gw -nd 2 -ph_reduce 1 -Ns 4 -do 1
After approximately 40 iterations the self-consistency is reached. Results are printed in the following files

• Aflex_... - The self-consistent local spectral function
• brisi.xxx - The spectral function and self-energy in each iteration

Information, printed to the standard output includes

• Difference = 9.86515e-05 is the difference between self-energies in the last two successive steps
• nd = 2; is the total impurity occupation
• mu = 1.50118; is the chemical potential
• alpha=0.2; is the mixing parameter used
• dmu=-1.99091e-07; if mu is changed in each iteration to get the desired doping (alpha_mu$>$0) this is the difference between last two chemical potentials

Finally, let me give some more information on the input parameters for the SUN flex program

• alpha: is the mixing parameter for the Green's function
• alpha_mu: is the mixing parameter for the chemical potential. If calculation is done at contant doping, chemical potential is adjusted in every step and alpha_mu is the corresponding mixing parameter. If it is set to zero, the calculation is done at fixed chemical potential.
• nd: desired total impurity occupation (relevant only if alpha_mu$>$0)
• ph_reduce: Particle hole channel gives unphysically large polarization $\chi$ for intermediate and large $U$. User can choose to reduce Coulomb repulsion $U$ in particle-hole channels by screening it with the particle-particle graphs: $U_{eff}= U/(1+U\chi^{pp}(0))$
• Na : The mesh used in calculating convolutions should be densed at two different localtion. Additional points are added to the neighborhood of the second peak or Fermi function. Then number of those additional points is Na.
• Ns : For SU(N) model it is just N.
• si : Instead of specifying input file, user can redirect certain output in the shell to the input of the program. In this case, -si switch should be used in the command line.
• max_diff: When the difference between two successive Green's functions is less than that number, the iteration is finished.
• max_steps: Iteration is never longer than max_steps to avoid infinite loops.
• ph: Every channel of the FLEX three channels can be switched on or off. If ph is set to 1(0), particle-hole ladder is included (excluded).
• pp: If pp is set to 1(0), particle-particle ladder is included (excluded).
• gw: If gw is set to 1(0), gw diagrams are included (excluded).
• g0: The diagrams can be evaluated with fully dressed propagators (electron Green's functions) or undressed propagators (only Hartree term self-consistently added). If g0 is set to 1, bare propagators are used, otherwise they are fully dressed.
• hs: If working at fix doping (alpha_mu$>$0) it is much easier to get converged results by fixing hartree term to the input $n$. The reason is that the results are very sensitive to the Hartree term and small change can result in numerical instability.
• do: If set to 1, there is much more output at each iteration