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error in routine broyden(6): factorization
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Joined: Mon Sep 03, 2018 8:37 am
Posts: 2
University: Peking University
error in routine broyden(6): factorization
Dear all,
I'm a new learner to EPW. When I try to do epw.x calculations, I met an error in the step of solving isotropic Eliashberg equations on imaginary-axis. I have 2 questions:
1. How to fix the error ' error in routine broyden(6): factorization' ?
2. Why the estimated Allen-Dynes Tc is so large ? What should I do to get the correct value?
Here are the input and output.

input:
Code:
--
&inputepw
prefix      = 'h3s',
amass(1)    = 1.008,
amass(2)    = 32.06
outdir      = './'

ep_coupling = .true.
elph        = .true.
kmaps       = .false.
epbwrite    = .true.

epwwrite = .true.

etf_mem     = 1

nbndsub     =  9
nbndskip    =  0

wannierize  = .true.
num_iter    = 10000
dis_win_max = 33.0
dis_win_min = 0.0
proj(1)='random'
!proj(2)     = 'S:p'
proj(2)     = 'H:s'

iverbosity  = 2

parallel_k  = .true.
parallel_q  = .false.

eps_acustic = 1.0
ephwrite    = .true.

fsthick     = 0.4
eptemp      = 300
degaussw    = 0.10
degaussq    = 0.5
nqstep      = 500

eliashberg  = .true.

liso = .true.
limag = .true.
lacon = .true.

conv_thr_iaxis = 1.0d-2
conv_thr_racon = 1.0d-2

wscut = 0.5

nstemp   = 3
tempsmin = 190.00
tempsmax = 240.00

nsiter   = 500

muc     = 0.16

dvscf_dir   = './save'

nk1         = 6
nk2         = 6
nk3         = 6

nq1         = 2
nq2         = 2
nq3         = 2

mp_mesh_k = .true.
nkf1        = 12
nkf2        = 12
nkf3        = 12

nqf1        = 12
nqf2        = 12
nqf3        = 12
/
4 cartesian
0.000000000   0.000000000   0.000000000
0.000000000   0.000000000  -0.500000000
0.000000000  -0.500000000  -0.500000000
-0.500000000  -0.500000000  -0.500000000

output:
Code:

......
......
===================================================================
Solve isotropic Eliashberg equations
===================================================================

Finish reading .freq file

Fermi level (eV) =     3.0765347476E+01
DOS(states/spin/eV/Unit Cell) =     1.4401140222E-02
Electron smearing (eV) =     1.0000000000E-01
Fermi window (eV) =     4.0000000000E-01
Nr irreducible k-points within the Fermi shell =         7 out of        84
2 bands within the Fermi window

Finish reading .egnv file

Max nr of q-points =        34

Finish reading .ikmap files

Start reading .ephmat files

Finish reading .ephmat files

lambda_max =             0.0450411   lambda_k_max =             0.0349339

Electron-phonon coupling strength =    0.0153917

Estimated Allen-Dynes Tc = 1304136.7081148 K for muc =    0.16000

Estimated BCS superconducting gap =     197.7921979 eV

temp(  1) =    190.00000 K

Solve isotropic Eliashberg equations on imaginary-axis

Total number of frequency points nsiw (      1 ) =      5

iter =      1   error =     2.4687234455E+03   Znormi(1) =     1.0000096887E+00   Deltai(1) =    -7.9926272214E-02
iter =      2   error =     3.1032568548E-05   Znormi(1) =     1.0000323260E+00   Deltai(1) =    -7.9923543453E-02
Convergence was reached in nsiter =      2

iaxis_imag   :      0.00s CPU      0.00s WALL (       1 calls)

Pade approximant of isotropic Eliashberg equations from imaginary-axis to real-axis

pade =      4   error =     9.6971175492E-04   Re[Znorm(1)] =     1.0000324395E+00   Re[Delta(1)] =    -7.9917933118E-02

raxis_pade   :      0.00s CPU      0.06s WALL (       1 calls)

Analytic continuation of isotropic Eliashberg equations from imaginary-axis to real-axis

Total number of frequency points nsw =   1000

iter =      1   error =     3.5303127519E+00   Re[Znorm(1)] =     1.0095012619E+00   Re[Delta(1)] =     3.0934545775E-02
iter =      2   error =     4.4514422372E-02   Re[Znorm(1)] =     1.0107920397E+00   Re[Delta(1)] =     3.1000378597E-02
iter =      3   error =     2.3226943841E-02   Re[Znorm(1)] =     1.0094155556E+00   Re[Delta(1)] =     3.1121693953E-02
iter =      4   error =     1.4163699664E-03   Re[Znorm(1)] =     1.0094607209E+00   Re[Delta(1)] =     3.1118151292E-02
Convergence was reached in nsiter =      4

raxis_acon   :      0.46s CPU      0.50s WALL (       1 calls)

itemp =   1   total cpu time :     0.6 secs

temp(  2) =    215.00000 K

Solve isotropic Eliashberg equations on imaginary-axis

Total number of frequency points nsiw (      2 ) =      4

iter =      1   error =     3.6474898270E+00   Znormi(1) =     1.0104612381E+00   Deltai(1) =     2.9609774910E-02
iter =      2   error =     1.8145447398E+01   Znormi(1) =     1.0143183603E+00   Deltai(1) =     1.5311049912E-03
iter =      3   error =     1.1027266065E+01   Znormi(1) =     1.0143319963E+00   Deltai(1) =    -1.5404809425E-04
iter =      4   error =     2.6237333860E+00   Znormi(1) =     1.0143320299E+00   Deltai(1) =     9.4249689740E-05
iter =      5   error =     2.6906797559E+01   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -3.6403709234E-06
iter =      6   error =     5.2143624565E+01   Znormi(1) =     1.0143320754E+00   Deltai(1) =     7.1038939502E-08
iter =      7   error =     7.2414067743E+00   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -1.1438373280E-08
iter =      8   error =     1.7121020893E+01   Znormi(1) =     1.0143320754E+00   Deltai(1) =     7.0686178910E-10
iter =      9   error =     5.5918259276E+01   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -1.2884922422E-11
iter =     10   error =     1.1674916477E+02   Znormi(1) =     1.0143320754E+00   Deltai(1) =     1.1042401721E-13
iter =     11   error =     3.2608593559E+02   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -4.1740120020E-16
iter =     12   error =     7.2644700849E+03   Znormi(1) =     1.0143320754E+00   Deltai(1) =     5.4313404221E-20
iter =     13   error =     9.4758877708E+00   Znormi(1) =     1.0143320754E+00   Deltai(1) =     5.6544495803E-21
iter =     14   error =     3.1271261124E+03   Znormi(1) =     1.0143320754E+00   Deltai(1) =     1.5729283948E-24
iter =     15   error =     1.5790915528E+03   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -1.4355529987E-27
iter =     16   error =     4.6182498842E+03   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -2.7129426882E-31
iter =     17   error =     2.2621787534E+04   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -1.1850080281E-35
iter =     18   error =     3.7699754882E+04   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -3.1010668206E-40
iter =     19   error =     7.6081446085E+04   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -4.3192551601E-45
iter =     20   error =     2.5811095566E+02   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -1.3195073361E-47
iter =     21   error =     1.1064835446E+02   Znormi(1) =     1.0143320754E+00   Deltai(1) =     1.2010977025E-49
iter =     22   error =     2.8294154637E+03   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -4.2471506223E-53
iter =     23   error =     5.0995761014E+03   Znormi(1) =     1.0143320754E+00   Deltai(1) =     8.3233123787E-57
iter =     24   error =     4.0748297992E+02   Znormi(1) =     1.0143320754E+00   Deltai(1) =     2.0294251698E-59
iter =     25   error =     2.3054296097E+02   Znormi(1) =     1.0143320754E+00   Deltai(1) =     8.7729024036E-62
iter =     26   error =     1.5360597909E+04   Znormi(1) =     1.0143320754E+00   Deltai(1) =     5.6867203476E-66
iter =     27   error =     4.0984645680E+03   Znormi(1) =     1.0143320754E+00   Deltai(1) =     1.3266819502E-69
iter =     28   error =     9.0543008089E+02   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -1.7051109766E-72
iter =     29   error =     1.0694719641E+02   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -1.4520313479E-74
iter =     30   error =     3.6912791082E+02   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -3.9212172986E-77
iter =     31   error =     9.0500315665E+02   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -4.3289705471E-80
iter =     32   error =     1.7397491957E+03   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -2.4887526622E-83
iter =     33   error =     3.3143472843E+03   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -7.5200225422E-87
iter =     34   error =     1.4183729964E+03   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -5.2789037394E-90
iter =     35   error =     2.2066633003E+03   Znormi(1) =     1.0143320754E+00   Deltai(1) =     2.3832886622E-93
iter =     36   error =     6.8285808331E+02   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -3.5043862381E-96
iter =     37   error =     5.5213745986E+02   Znormi(1) =     1.0143320754E+00   Deltai(1) =     6.3182051807E-99
iter =     38   error =     1.7660910107E+02   Znormi(1) =     1.0143320754E+00   Deltai(1) =     3.4704250772-101
iter =     39   error =     2.3623341737E+02   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -8.5142226839-104
iter =     40   error =     7.5477225197E+00   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -2.0277536460-104
iter =     41   error =     3.1199926982E+03   Znormi(1) =     1.0143320754E+00   Deltai(1) =     6.3583812063-108
iter =     42   error =     1.4744014679E+03   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -4.3198221105-111
iter =     43   error =     3.1923011944E+03   Znormi(1) =     1.0143320754E+00   Deltai(1) =     1.3521215438-114
iter =     44   error =     2.0201245912E+03   Znormi(1) =     1.0143320754E+00   Deltai(1) =    -6.7050212014-118

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Error in routine broyden (6):
factorization
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

stopping ...

Thanks and regards,
Xiaohan

Tue Sep 04, 2018 3:27 am

Joined: Fri Jan 22, 2016 6:48 pm
Posts: 144
University: SUNY-Binghamton
Re: error in routine broyden(6): factorization
Dear Xiaohan,

1. You can lower the broyden_beta parameter (default value 0.7). However, in your case the code is crashing most likely because you are attempting to solve the Eliashberg equation at temperatures greater than the Tc (estimated Tc based on Allen-Dynes is 197 K). You should start solving the equations from lower temperatures and look at the temperature dependence of the superconducting gap [look for instance at Fig. 4a in PHYSICAL REVIEW B 87, 024505 (2013)].

2. I would guess that your calculations may not be converged. You need to converge the e-ph coupling strength with respect to the k and q-meshes. The Allen-Dynes expression on Tc also depends on which value you use for the Coulomb parameter mu*.

Best,
Roxana

_________________
Roxana Margine
Associate Professor
Department of Physics, Applied Physics and Astronomy
Binghamton University, State University of New York
PO Box 6000
Binghamton, NY 13902-6000

Wed Sep 05, 2018 4:26 pm

Joined: Mon Sep 03, 2018 8:37 am
Posts: 2
University: Peking University
Re: error in routine broyden(6): factorization
Dear Roxana,

Thank you very much for your reply.
The first problem is truly due to that the temperature is greater than the Tc.
And the second problem is more likely related to my wrong setting of nbndsub and nbndskip. I recalculated epw with the same k , q points and muc as the article (https://arxiv.org/abs/1606.09477 ). I set nbndsub=12 , nbndskip=4 . And the Tc is 118K, which is still smaller than that in the article(166K).
So I want to ask what other converge tests should I take?About which parameters?
Thanks again.

Best,
Xiaohan

Fri Sep 14, 2018 2:38 am

Joined: Fri Jan 22, 2016 6:48 pm
Posts: 144
University: SUNY-Binghamton
Re: error in routine broyden(6): factorization
Dear Xiaohan,

For example you can check if the wannierization is correct (e.g, band structure after wannier interpolation) or if the decay of the Hamiltonian, dynamical matrix e-ph matrix elements are good enough [see Computer Physics Communications 181 (2010) 2140–2148].

Best,
Roxana

_________________
Roxana Margine
Associate Professor
Department of Physics, Applied Physics and Astronomy
Binghamton University, State University of New York
PO Box 6000
Binghamton, NY 13902-6000

Mon Sep 17, 2018 2:54 pm
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