Slow DMFT calculations for a 5-orbital system (FeSb2)

[shinaoka]

I've created a new issue (following #81 ).

What is the local site symmetry of FeSb2?
According to the output of dcore_pre, the five orbitals are not degenerate and
the site symmetry is quite low.

eigenvalues:  [12.45711142 12.45711142 13.37845212 13.37845212 13.67358996 13.67358996
 13.74709092 13.74709092 14.35796558 14.35796558]

If this is true, this could be very problematic to any matrix CT-HYB solvers like (ALPS/CT-HYB, triqs/cthyb) because they use the site symmetry to reduce the computational cost.
According to the output of the ALPS/CT-HYB,
the dimension of the largest subspace of the local Hilbert space is 100 (could be too large).

There are several possible workarounds.

• Use density-density interaction and use segment code (ALPS/CT-HYB-SEGMENT) supported by DCore
• Truncate the local Hilbert space (supported by ALPS/CT-HYB)

What do you think?

Sector 0 : dim = 1, min energy = 45.5274, max energy = 45.5274
Sector 1 : dim = 5, min energy = 27.6395, max energy = 29.5404
Sector 2 : dim = 5, min energy = 27.6395, max energy = 29.5404
Sector 3 : dim = 25, min energy = 12.3626, max energy = 20.7725
Sector 4 : dim = 10, min energy = 12.3626, max energy = 14.632
Sector 5 : dim = 50, min energy = -0.840933, max energy = 8.01558
Sector 6 : dim = 10, min energy = 12.3626, max energy = 14.632
Sector 7 : dim = 50, min energy = -0.840933, max energy = 8.01558
Sector 8 : dim = 100, min energy = -11.7493, max energy = 3.7755
Sector 9 : dim = 10, min energy = -0.840933, max energy = 1.42856
Sector 10 : dim = 50, min energy = -11.7493, max energy = -2.85001
Sector 11 : dim = 100, min energy = -19.7363, max energy = -5.15018
Sector 12 : dim = 10, min energy = -0.840933, max energy = 1.42856
Sector 13 : dim = 50, min energy = -11.7493, max energy = -2.85001
Sector 14 : dim = 100, min energy = -19.7363, max energy = -5.15018
Sector 15 : dim = 100, min energy = -20.6242, max energy = -5.36257
Sector 16 : dim = 5, min energy = -11.7493, max energy = -9.84843
Sector 17 : dim = 25, min energy = -19.7363, max energy = -11.5884
Sector 18 : dim = 50, min energy = -20.6242, max energy = -11.9436
Sector 19 : dim = 50, min energy = -18.9011, max energy = -10.2168
Sector 20 : dim = 5, min energy = -11.7493, max energy = -9.84843
Sector 21 : dim = 25, min energy = -19.7363, max energy = -11.5884
Sector 22 : dim = 50, min energy = -20.6242, max energy = -11.9436
Sector 23 : dim = 50, min energy = -18.9011, max energy = -10.2168
Sector 24 : dim = 25, min energy = -15.1046, max energy = -6.61754
Sector 25 : dim = 1, min energy = -19.7363, max energy = -19.7363
Sector 26 : dim = 5, min energy = -20.6242, max energy = -18.7233
Sector 27 : dim = 10, min energy = -18.9011, max energy = -16.6317
Sector 28 : dim = 10, min energy = -15.1046, max energy = -12.8351
Sector 29 : dim = 5, min energy = -9.01299, max energy = -7.11214
Sector 30 : dim = 1, min energy = -19.7363, max energy = -19.7363
Sector 31 : dim = 5, min energy = -20.6242, max energy = -18.7233
Sector 32 : dim = 10, min energy = -18.9011, max energy = -16.6317
Sector 33 : dim = 10, min energy = -15.1046, max energy = -12.8351
Sector 34 : dim = 5, min energy = -9.01299, max energy = -7.11214

[ZhijieFan]

Hi,

I agree with you. The sysmetry might not be correct in the hr.dat file. The wannierization is performed by another team. In their input for wannier90, I see that site_symmetry is not used. If I understand the structure of FeSb2 correctly, the two Fe atoms in the unit cells are equivalent under certain symmetry operations.

I also figured that the wannierization result FeSb2_hr.dat have complex values which is considered as not good by the triqs/dft_tools. Will this also affect performance of the solver?

Best,
Zhijie

[shinaoka]

Hi,

The output of dcore_pre also indicates that the intra-atom part of the hopping matrix for the two atoms are not equivalent.
For DCore, any inequivalent shells must be connected by the "identity" transformation in the hopping file.

If SOI is not important, you could construct non-spinor Wannier functions.

---intra shell Hamiltonian (w/o local potential)
    ordering: up ... up, down ... down
     corr_shell= 0
      ( 1.38e+01, 0.00e+00) ( 2.46e-02, 1.20e-05) (-9.23e-03,-9.00e-06) ( 7.02e-02, 2.10e-05) ( 1.77e-01,-1.50e-05)   ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)
      ( 2.46e-02,-1.20e-05) ( 1.25e+01, 0.00e+00) ( 8.83e-02,-4.30e-05) (-1.43e-02, 1.80e-05) (-3.26e-02, 6.40e-05)   ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)
      (-9.23e-03, 9.00e-06) ( 8.83e-02, 4.30e-05) ( 1.37e+01, 0.00e+00) (-3.94e-03,-1.00e-06) (-8.05e-03, 2.00e-06)   ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)
      ( 7.02e-02,-2.10e-05) (-1.43e-02,-1.80e-05) (-3.94e-03, 1.00e-06) ( 1.35e+01, 0.00e+00) ( 2.78e-01,-1.25e-04)   ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)
      ( 1.77e-01, 1.50e-05) (-3.26e-02,-6.40e-05) (-8.05e-03,-2.00e-06) ( 2.78e-01, 1.25e-04) ( 1.42e+01, 0.00e+00)   ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)

      ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)   ( 1.38e+01, 0.00e+00) ( 2.46e-02, 1.20e-05) (-9.23e-03,-9.00e-06) ( 7.02e-02, 2.10e-05) ( 1.77e-01,-1.50e-05)
      ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)   ( 2.46e-02,-1.20e-05) ( 1.25e+01, 0.00e+00) ( 8.83e-02,-4.30e-05) (-1.43e-02, 1.80e-05) (-3.26e-02, 6.40e-05)
      ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)   (-9.23e-03, 9.00e-06) ( 8.83e-02, 4.30e-05) ( 1.37e+01, 0.00e+00) (-3.94e-03,-1.00e-06) (-8.05e-03, 2.00e-06)
      ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)   ( 7.02e-02,-2.10e-05) (-1.43e-02,-1.80e-05) (-3.94e-03, 1.00e-06) ( 1.35e+01, 0.00e+00) ( 2.78e-01,-1.25e-04)
      ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)   ( 1.77e-01, 1.50e-05) (-3.26e-02,-6.40e-05) (-8.05e-03,-2.00e-06) ( 2.78e-01, 1.25e-04) ( 1.42e+01, 0.00e+00)

      eigenvalues:  [12.45711142 12.45711142 13.37845212 13.37845212 13.67358996 13.67358996
 13.74709092 13.74709092 14.35796558 14.35796558]

     corr_shell= 1
      ( 1.38e+01, 0.00e+00) (-8.55e-03,-2.00e-06) ( 6.62e-03,-4.00e-06) ( 7.06e-02, 7.00e-06) (-1.79e-01, 2.20e-05)   ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)
      (-8.55e-03, 2.00e-06) ( 1.25e+01, 0.00e+00) (-8.84e-02,-1.00e-06) (-8.24e-03, 4.00e-06) ( 2.33e-02, 2.10e-05)   ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)
      ( 6.62e-03, 4.00e-06) (-8.84e-02, 1.00e-06) ( 1.37e+01, 0.00e+00) ( 3.97e-03, 8.00e-06) (-7.17e-03,-1.60e-05)   ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)
      ( 7.06e-02,-7.00e-06) (-8.24e-03,-4.00e-06) ( 3.97e-03,-8.00e-06) ( 1.35e+01, 0.00e+00) (-2.78e-01, 1.15e-04)   ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)
      (-1.79e-01,-2.20e-05) ( 2.33e-02,-2.10e-05) (-7.17e-03, 1.60e-05) (-2.78e-01,-1.15e-04) ( 1.42e+01, 0.00e+00)   ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)

      ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)   ( 1.38e+01, 0.00e+00) (-8.55e-03,-2.00e-06) ( 6.62e-03,-4.00e-06) ( 7.06e-02, 7.00e-06) (-1.79e-01, 2.20e-05)
      ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)   (-8.55e-03, 2.00e-06) ( 1.25e+01, 0.00e+00) (-8.84e-02,-1.00e-06) (-8.24e-03, 4.00e-06) ( 2.33e-02, 2.10e-05)
      ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)   ( 6.62e-03, 4.00e-06) (-8.84e-02, 1.00e-06) ( 1.37e+01, 0.00e+00) ( 3.97e-03, 8.00e-06) (-7.17e-03,-1.60e-05)
      ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)   ( 7.06e-02,-7.00e-06) (-8.24e-03,-4.00e-06) ( 3.97e-03,-8.00e-06) ( 1.35e+01, 0.00e+00) (-2.78e-01, 1.15e-04)
      ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00) ( 0.00e+00, 0.00e+00)   (-1.79e-01,-2.20e-05) ( 2.33e-02,-2.10e-05) (-7.17e-03, 1.60e-05) (-2.78e-01,-1.15e-04) ( 1.42e+01, 0.00e+00)

      eigenvalues:  [12.45704916 12.45704916 13.37826799 13.37826799 13.67344755 13.67344755
 13.74699307 13.74699307 14.35769523 14.35769523]