Analytical continuation
Below we describe how to used
the analytical continuation program. Because of nonanalyticity
of QMC results one cannot make direct (like Pade) analytical continuation from
Matsubara to real axis. What we do in practice we make the analytical
continuation of Green function from imaginary time axis to real axis using
Maximum Entropy (ME) method. Then using this GF and Hilbert transformation
formulae one solve this equation (Hilbert) for the selfenergy.
Below we describe input and output parameter
for analytical continuation program.
File inpmax:
2
64
1 0.003
16.0
300
0.02
3000
1200
1
1234
0
0.040 8.7
4. 
! Ns ! L ! idg, deltaG (0  propotional
G, 1 = const) !
Beta ! Ne ! De ! Nmc ! iflat,eim !mu U 


The first line number of bands 1,2,3 … In our case bands are degenerate one band is enough.
The second line is number of time slices used (it is defined in QMC program). Idg is the way the model function for ME method is
build. From our experience follows that constant model function is the best
one. DeltaG is deviation from GF (0.0010.005 is usual interval we
worked with). The forth line is clear – inverse temperature. Ne is number of points on real axis (maximum 600)
and de is frequency step on real axis: de*Ne=energy
window on real axis. Nmc is number of
annealing steps. 1200 is alpha coefficient (recall exponent in ME method). The
ninth line is number of smoothing runs. Tenth line is random seed number. Iflat is flat model which is used in ME method (zero
corresponds to constant and 1 corresponds to other model
which was based on Pade approximation, but it us better always to keep zero). Eim is connected to the first model described and if
one takes zero then eim is irrelevant. The
last line is the chemical potential, Coulomb repulsion.
Another input file called Gtau1.dat contains GF on imaginary axis.
Output files are “dos”
which contains DOS.