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[doc] corrections to tutorials

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Leonid Pourovskii 2015-03-18 20:54:07 +01:00
parent 54caa08069
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5 changed files with 96 additions and 94 deletions
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46
doc/Ce-HI.rst
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@ -95,23 +95,16 @@ where the solver is initialized with the value of `beta`, and the orbital quantu
The Hubbard-I initialization `Solver` has also optional parameters one may use:
* `n_msb`: the number of Matsubara frequencies used. The default is `n_msb=1025`.
* `use_spin_orbit`: if set 'True' the solver is run with spin-orbit coupling
included. To perform actual DFT+DMFT calculations with spin-orbit one should
also run :program:`Wien2k` and :program:`dmftproj` in spin-polarized mode and
with spin-orbit included. By default, `use_spin_orbit=False`.
* `use_spin_orbit`: if set 'True' the solver is run with spin-orbit coupling included. To perform actual DFT+DMFT calculations with spin-orbit one should also run :program:`Wien2k` and :program:`dmftproj` in spin-polarized mode and with spin-orbit included. By default, `use_spin_orbit=False`.
* `Nmoments`: the number of moments used to describe high-ferquency tails of the Hubbard-I Green's function and self-energy. By default `Nmoments = 5`
The `Solver.solve(U_int, J_hund)` statement has two necessary parameters, the
Hubbard U parameter `U_int` and Hund's rule coupling `J_hund`. Notice that the
solver constructs the full 4-index `U`-matrix by default, and the `U_int` parameter
is in fact the Slatter `F0` integral. Other optional parameters are:
The `Solver.solve(U_int, J_hund)` statement has two necessary parameters, the Hubbard U parameter `U_int` and Hund's rule coupling `J_hund`. Notice that the solver constructs the full 4-index `U`-matrix by default, and the `U_int` parameter is in fact the Slatter `F0` integral. Other optional parameters are:
* `T`: matrix that transforms the interaction matrix from complex spherical
harmonics to a symmetry adapted basis. By default, the complex spherical harmonics
basis is used and `T=None`.
* `verbosity`: tunes output from the solver. If `verbosity=0` only basic
information is printed, if `verbosity=1` the ground state atomic occupancy and
its energy are printed, if `verbosity=2` additional information is printed for
all occupancies that were diagonalized. By default, `verbosity=0`.
* `T`: matrix that transforms the interaction matrix from complex spherical harmonics to a symmetry adapted basis. By default, the complex spherical harmonics basis is used and `T=None`.
* `verbosity`: tunes output from the solver. If `verbosity=0` only basic information is printed, if `verbosity=1` the ground state atomic occupancy and its energy are printed, if `verbosity=2` additional information is printed for all occupancies that were diagonalized. By default, `verbosity=0`.
* `Iteration_Number`: the iteration number of the DMFT loop. Used only for printing. By default `Iteration_Number=1`
* `Test_Convergence`: convergence criterion. Once the self-energy is converged below `Test_Convergence` the Hubbard-I solver is not called anymore. By default `Test_Convergence=0.0001`.
We need also to introduce some changes in the DMFT loop with respect that used for CT-QMC calculations in :ref:`advanced`.
The hybridization function is neglected in the Hubbard-I approximation, and only non-interacting level
@ -160,22 +153,23 @@ use here the default convergence criterion in :program:`Wien2k` (convergence to
After calculations are done we may check the value of correlation ('Hubbard') energy correction to the total energy::
>grep HUBBARD Ce-gamma.scf|tail -n 1
HUBBARD ENERGY(included in SUM OF EIGENVALUES): -0.220502
HUBBARD ENERGY(included in SUM OF EIGENVALUES): -0.012866
and the band ("kinetic") energy with DMFT correction::
In the case of Ce, with the correlated shell occupancy close to 1 the Hubbard energy is close to 0, while the DC correction to energy is about J/4 in accordance with the fully-localized-limit formula, hence, giving the total correction :math:`\Delta E_{HUB}=E_{HUB}-E_{DC} \approx -J/4`, which is in our case is equal to -0.175 eV :math:`\approx`-0.013 Ry.
The band ("kinetic") energy with DMFT correction is ::
>grep DMFT Ce-gamma.scf |tail -n 1
KINETIC ENERGY with DMFT correction: -5.329087
KINETIC ENERGY with DMFT correction: -5.370632
as well as the convergence in total energy::
One may also check the convergence in total energy::
>grep :ENE Ce-gamma.scf |tail -n 5
:ENE : ********** TOTAL ENERGY IN Ry = -17717.77119670
:ENE : ********** TOTAL ENERGY IN Ry = -17717.77050935
:ENE : ********** TOTAL ENERGY IN Ry = -17717.77040176
:ENE : ********** TOTAL ENERGY IN Ry = -17717.77020712
:ENE : ********** TOTAL ENERGY IN Ry = -17717.77037540
:ENE : ********** TOTAL ENERGY IN Ry = -17717.56318334
:ENE : ********** TOTAL ENERGY IN Ry = -17717.56342250
:ENE : ********** TOTAL ENERGY IN Ry = -17717.56271503
:ENE : ********** TOTAL ENERGY IN Ry = -17717.56285812
:ENE : ********** TOTAL ENERGY IN Ry = -17717.56287381
Calculating DOS with Hubbard-I
------------------------------
@ -197,7 +191,7 @@ Then one needs to load projectors needed for calculations of corresponding proje
SK = SumkDFTTools(hdf_file=dft_filename+'.h5', use_dft_blocks=False)
Then after the solver initialization and setting up atomic levels we compute atomic Green's function and self-energy on the real axis::
Then after the solver initialization we load the previously calculated chemical potential and double-counting correction. Having set up atomic levels we then compute the atomic Green's function and self-energy on the real axis::
S.set_atomic_levels( eal = eal )
S.GF_realomega(ommin=ommin, ommax = ommax, N_om=N_om,U_int=U_int,J_hund=J_hund)

1
doc/Ce-gamma.indmftpr
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@ -6,4 +6,3 @@ complex
0 0 0 0 ! l included for each sort
0
-.40 0.40 ! Energy window relative to E_f

116
doc/Ce-gamma.py
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@ -2,25 +2,23 @@ from pytriqs.applications.dft.sumk_dft import *
from pytriqs.applications.dft.converters.wien2k_converter import *
from pytriqs.applications.impurity_solvers.hubbard_I.hubbard_solver import Solver
dft_filename = 'Ce-gamma'
lda_filename = 'Ce-gamma'
beta = 40
U_int = 6.00
J_hund = 0.70
Loops = 2 # Number of DMFT sc-loops
Loops = 5 # Number of DMFT sc-loops
Mix = 0.7 # Mixing factor in QMC
# 1.0 ... all from imp; 0.0 ... all from Gloc
DC_type = 0 # 0...FLL, 1...Held, 2... AMF, 3...Lichtenstein
useBlocs = False # use bloc structure from DFT input
DC_Mix = 1.0 # 1.0 ... all from imp; 0.0 ... all from Gloc
useBlocs = False # use bloc structure from LDA input
useMatrix = True # use the U matrix calculated from Slater coefficients instead of (U+2J, U, U-J)
Natomic = 1
chemical_potential_init=0.0 # initial chemical potential
HDFfilename = dft_filename+'.h5'
use_val= U_int * (Natomic - 0.5) - J_hund * (Natomic * 0.5 - 0.5)
HDFfilename = lda_filename+'.h5'
# Convert DMFT input:
# Can be commented after the first run
Converter = Wien2kConverter(filename=dft_filename)
Converter = Wien2kConverter(filename=lda_filename)
Converter.convert_dft_input()
#check if there are previous runs:
@ -42,23 +40,30 @@ previous_runs = mpi.bcast(previous_runs)
previous_present = mpi.bcast(previous_present)
# Init the SumK class
SK=SumkDFT(hdf_file=dft_filename+'.h5',use_dft_blocks=False)
SK=SumkDFT(hdf_file=lda_filename+'.h5',use_dft_blocks=False)
Norb = SK.corr_shells[0]['dim']
l = SK.corr_shells[0]['l']
# Init the Solver:
# Init the Hubbard-I solver:
S = Solver(beta = beta, l = l)
chemical_potential=chemical_potential_init
# load previous data: old self-energy, chemical potential, DC correction
if (previous_present):
# load previous data:
mpi.report("Using stored data for initialisation")
if (mpi.is_master_node()):
ar = HDFArchive(HDFfilename,'a')
S.Sigma << ar['SigmaImFreq']
S.Sigma <<= ar['SigmaF']
del ar
things_to_load=['chemical_potential','dc_imp']
old_data=SK.load(things_to_load)
chemical_potential=old_data[0]
SK.dc_imp=old_data[1]
S.Sigma = mpi.bcast(S.Sigma)
SK.load()
chemical_potential=mpi.bcast(chemical_potential)
SK.dc_imp=mpi.bcast(SK.dc_imp)
# DMFT loop:
for Iteration_Number in range(1,Loops+1):
@ -69,84 +74,77 @@ for Iteration_Number in range(1,Loops+1):
SK.put_Sigma(Sigma_imp = [ S.Sigma ])
# Compute the SumK, possibly fixing mu by dichotomy
if SK.density_required and (Iteration_Number > 0):
Chemical_potential = SK.calc_mu( precision = 0.01 )
if SK.density_required and (Iteration_Number > 1):
chemical_potential = SK.calc_mu( precision = 0.000001 )
else:
mpi.report("No adjustment of chemical potential\nTotal density = %.3f"%SK.total_density(mu=Chemical_potential))
mpi.report("No adjustment of chemical potential\nTotal density = %.3f"%SK.total_density(mu=chemical_potential))
# Density:
S.G << SK.extract_G_loc()[0]
S.G <<= SK.extract_G_loc()[0]
mpi.report("Total charge of Gloc : %.6f"%S.G.total_density())
dm = S.G.density()
# calculated DC at the first run to have reasonable initial non-interacting atomic level positions
if ((Iteration_Number==1)and(previous_present==False)):
SK.calc_dc( dens_mat=dm, U_interact = U_int, J_hund = J_hund, orb = 0, use_dc_formula = DC_type, use_val=use_val)
dc_value_init=U_int/2.0
dm=S.G.density()
SK.calc_dc( dm, U_interact = U_int, J_hund = J_hund, orb = 0, use_dc_formula = DC_type, use_dc_value=dc_value_init)
# set atomic levels:
# calculate non-interacting atomic level positions:
eal = SK.eff_atomic_levels()[0]
S.set_atomic_levels( eal = eal )
# update hdf5
if (mpi.is_master_node()):
ar = HDFArchive(HDFfilename,'a')
ar['Chemical_Potential%s'%itn] = Chemical_potential
del ar
# solve it:
S.solve(U_int = U_int, J_hund = J_hund, verbosity = 1)
if (mpi.is_master_node()):
ar = HDFArchive(HDFfilename)
ar['iterations'] = itn
# Now mix Sigma and G:
if ((itn>1)or(previous_present)):
if (mpi.is_master_node()and (Mix<1.0)):
ar = HDFArchive(HDFfilename,'r')
mpi.report("Mixing Sigma and G with factor %s"%Mix)
if ('SigmaImFreq' in ar):
S.Sigma << Mix * S.Sigma + (1.0-Mix) * ar['SigmaImFreq']
if ('SigmaF' in ar):
S.Sigma <<= Mix * S.Sigma + (1.0-Mix) * ar['SigmaF']
if ('GF' in ar):
S.G << Mix * S.G + (1.0-Mix) * ar['GF']
S.G <<= Mix * S.G + (1.0-Mix) * ar['GF']
del ar
S.G = mpi.bcast(S.G)
S.Sigma = mpi.bcast(S.Sigma)
if (mpi.is_master_node()):
ar['SigmaImFreq'] = S.Sigma
ar['GF'] = S.G
# after the Solver has finished, set new double counting:
dm = S.G.density()
SK.calc_dc( dm, U_interact = U_int, J_hund = J_hund, orb = 0, use_dc_formula = DC_type , use_val=use_val)
SK.calc_dc( dm, U_interact = U_int, J_hund = J_hund, orb = 0, use_dc_formula = DC_type )
# correlation energy calculations:
correnerg = 0.5 * (S.G * S.Sigma).total_density()
mpi.report("Corr. energy = %s"%correnerg)
# store the impurity self-energy, GF as well as correlation energy in h5
if (mpi.is_master_node()):
ar = HDFArchive(HDFfilename,'a')
ar['iterations'] = itn
ar['chemical_cotential%s'%itn] = chemical_potential
ar['SigmaF'] = S.Sigma
ar['GF'] = S.G
ar['correnerg%s'%itn] = correnerg
ar['DCenerg%s'%itn] = SK.dc_energ
del ar
#Save stuff:
SK.save(['chemical_potential','dc_imp','dc_energ'])
#Save essential SumkDFT data:
things_to_save=['chemical_potential','dc_energ','dc_imp']
SK.save(things_to_save)
if (mpi.is_master_node()):
print 'DC after solver: ',SK.dc_imp[SK.invshellmap[0]]
print 'DC after solver: ',SK.dc_imp[0]
# do some analysis:
# print out occupancy matrix of Ce 4f
mpi.report("Orbital densities of impurity Green function:")
dm1 = S.G.density()
for s in dm1:
for s in dm:
mpi.report("Block %s: "%s)
for ii in range(len(dm1[s])):
for ii in range(len(dm[s])):
str = ''
for jj in range(len(dm1[s])):
if (dm1[s][ii,jj].real>0):
str += " %.4f"%(dm1[s][ii,jj].real)
for jj in range(len(dm[s])):
if (dm[s][ii,jj].real>0):
str += " %.4f"%(dm[s][ii,jj].real)
else:
str += " %.4f"%(dm1[s][ii,jj].real)
str += " %.4f"%(dm[s][ii,jj].real)
mpi.report(str)
mpi.report("Total charge of impurity problem : %.6f"%S.G.total_density())
@ -154,11 +152,13 @@ for Iteration_Number in range(1,Loops+1):
# find exact chemical potential
if (SK.density_required):
SK.chemical_potential = SK.calc_mu( precision = 0.000001 )
dN,d = SK.calc_density_correction(filename = dft_filename+'.qdmft')
# calculate and save occupancy matrix in the Bloch basis for Wien2k charge denity recalculation
dN,d = SK.calc_density_correction(filename = lda_filename+'.qdmft')
mpi.report("Trace of Density Matrix: %s"%d)
#correlation energy:
# store correlation energy contribution to be read by Wien2ki and then included to DFT+DMFT total energy
if (mpi.is_master_node()):
ar = HDFArchive(HDFfilename)
itn = ar['iterations']
@ -166,6 +166,6 @@ if (mpi.is_master_node()):
DCenerg = ar['DCenerg%s'%itn]
del ar
correnerg -= DCenerg[0]
f=open(dft_filename+'.qdmft','a')
f=open(lda_filename+'.qdmft','a')
f.write("%.16f\n"%correnerg)
f.close()

25
doc/Ce-gamma_DOS.py
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@ -20,7 +20,6 @@ broadening = 0.02
HDFfilename = dft_filename+'.h5'
# Convert DMFT input:
# Can be commented after the first run
Converter = Wien2kConverter(filename=dft_filename,repacking=True)
Converter.convert_dft_input()
Converter.convert_parproj_input()
@ -30,7 +29,7 @@ previous_runs = 0
previous_present = False
if mpi.is_master_node():
ar = HDFArchive(HDFfilename,'a')
ar = HDFArchive(HDFfilename)
if 'iterations' in ar:
previous_present = True
previous_runs = ar['iterations']
@ -43,27 +42,37 @@ mpi.barrier()
previous_runs = mpi.bcast(previous_runs)
previous_present = mpi.bcast(previous_present)
# if previous runs are present, no need for recalculating the bloc structure
# It has to be commented, if you run this script for the first time, starting
# from a converted h5 archive.
# Init the SumK class
SK = SumkDFTTools(hdf_file=dft_filename+'.h5',use_dft_blocks=False)
# load old chemical potential and DC
chemical_potential=0.0
if mpi.is_master_node():
ar = HDFArchive(HDFfilename)
things_to_load=['chemical_potential','dc_imp']
old_data=SK.load(things_to_load)
chemical_potential=old_data[0]
SK.dc_imp=old_data[1]
SK.chemical_potential=mpi.bcast(chemical_potential)
SK.dc_imp=mpi.bcast(SK.dc_imp)
if (mpi.is_master_node()):
print 'DC after reading SK: ',SK.dc_imp[SK.invshellmap[0]]
print 'DC after reading SK: ',SK.dc_imp[0]
N = SK.corr_shells[0]['dim']
l = SK.corr_shells[0]['l']
# Init the Solver:
S = Solver(beta = Beta, l = l)
S.Nmoments= 8
# set atomic levels:
eal = SK.eff_atomic_levels()[0]
S.set_atomic_levels( eal = eal )
# Run the solver to get GF and self-energy on the real axis
S.GF_realomega(ommin=ommin, ommax = ommax, N_om=N_om,U_int=U_int,J_hund=J_hund)
SK.put_Sigma(Sigma_imp = [S.Sigma])
# compute DOS
SK.dos_partial(broadening=broadening)

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