Multiple impurities calculations (Difficulty reproducing metallic DMFT solution for LixMnO2)

[mlei012]

Hi everyone,

I am trying to reproduce the DMFT results for LixMnO2 reported in this PRB paper. (https://journals.aps.org/prb/abstract/10.1103/PhysRevB.108.165124)

According to Fig. 3 of the paper, for x = 0.83 and x = 0.17, a paramagnetic DMFT calculation with 4 inequivalent Mn impurities leads to a metallic solution with a finite quasiparticle weight.

However, in my calculations, the DMFT self-consistency always converges to an insulating solution (G(beta/2) ≈ 0 for all impurities).

My workflow is:
Quantum ESPRESSO → Wannier90 → solid_dmft

In Quantum Espresso, I set nspin = 1 and without using GGA+U

Here are the density of states

In Wannier90, I use

num_bands         =   128
num_wann          =   30

dis_win_min       = 0
dis_win_max       = 11
dis_froz_min      = 6
dis_froz_max      = 11
dis_num_iter      =  500

fermi_energy      = 6.9324

num_iter          = 500
dis_mix_ratio = 1.0
search_shells = 64

write_hr = true

begin projections
Mn:d
end projections

ATOMIC_POSITIONS crystal
Mn    0.1673062875404817  0.0000000000000000  0.8384597873595114
Mn    0.8326937124595184 -0.0000000000000000  0.1615402126404890
Mn    0.1721776229506156  0.5000000000000000  0.3378448662585413
Mn    0.8278223770493841  0.5000000000000000  0.6621551337414588
Mn    0.5000000000000000  0.0000000000000000  0.5000000000000000
Mn    0.5000000000000000  0.5000000000000000  0.0000000000000000
  O    0.0988366466508028  0.0000000000000000  0.1993336633874058
  O    0.2380293561555444 -0.0000000000000000  0.4911933411464841
  O    0.4347515229381831  0.0000000000000000  0.8342703302803434
  O    0.9011633533491972 -0.0000000000000000  0.8006663366125943
  O    0.7619706438444552  0.0000000000000000  0.5088066588535164
  O    0.5652484770618166 -0.0000000000000000  0.1657296697196569
  O    0.0989523772222211  0.5000000000000000  0.6585834918173139
  O    0.2320239768641581  0.5000000000000000  0.0045623536489733
  O    0.4347357622691962  0.5000000000000000  0.3342059587587505
  O    0.9010476227777793  0.5000000000000000  0.3414165081826861
  O    0.7679760231358421  0.5000000000000000 -0.0045623536489732
  O    0.5652642377308040  0.5000000000000000  0.6657940412412497
 Li     0.0000000000000000  0.0000000000000000  0.5000000000000000

The solid_dmft parameters are

[general]
seedname = "LMO"
jobname = "DMFT"
enforce_off_diag = true
block_threshold = 0.008
set_rot = "hloc"

prec_mu = 0.001

h_int_type = "density_density"
U = 4.5
J = 0.5

mu_initial_guess = -0.5

beta = 40

n_iter_dmft = 30

dc_type = 0
dc = true
dc_dmft = true

calc_energies = false
sigma_mix = 1.0
mu_mix_const = 0.7

h5_save_freq = 1

[solver]
type = "cthyb"
n_l = 50
length_cycle = 200
n_warmup_cycles = 50000
n_cycles_tot = 2e+7
imag_threshold = 1e-5
measure_G_l = false

perform_tail_fit = true
fit_max_moment = 2
fit_min_w = 30
fit_max_w = 90

However, after only 5 iterations, the system becomes an insulator

============================================================
summary of impurity observables:
total occupany of impurity 0:  3.9210
total occupany of impurity 1:  3.9757
total occupany of impurity 2:  4.0038
total occupany of impurity 3:  4.0047
G(beta/2) occ of impurity 0:  -0.0000
G(beta/2) occ of impurity 1:  -0.0000
G(beta/2) occ of impurity 2:  -0.0000
G(beta/2) occ of impurity 3:  -0.0000
Z (simple estimate) of impurity 0 per orb:
   up:  0.054  0.026  0.025  0.113  0.933
 down:  0.054  0.026  0.025  0.113  0.933
Z (simple estimate) of impurity 1 per orb:
   up:  0.032  0.884  0.033  0.950  0.958
 down:  0.032  0.884  0.033  0.950  0.958
Z (simple estimate) of impurity 2 per orb:
   up:  0.898  0.034  0.035  0.959  0.961
 down:  0.898  0.034  0.035  0.959  0.961
Z (simple estimate) of impurity 3 per orb:
   up:  0.904  0.015  0.016  0.960  0.962
 down:  0.904  0.015  0.016  0.960  0.962
============================================================

============================================================
convergence:
δμ:      1.3222e-02
Impurity 0:
δn imp : 4.9344e-02
δn orb : 7.4726e-03  4.6053e-03  2.1156e-02  2.3809e-02  1.6457e-02
δ Gimp : 6.6658e-03
δ G0   : 7.4286e-04
δ Σ    : 4.3216e+00
Impurity 1:
δn imp : 8.6767e-03
δn orb : 1.9173e-02  7.8675e-03  1.9826e-04  3.5038e-03  1.4662e-02
δ Gimp : 4.5592e-03
δ G0   : 5.3862e-04
δ Σ    : 7.8571e+00
Impurity 2:
δn imp : 3.3942e-02
δn orb : 1.9069e-02  8.2418e-03  1.8859e-02  1.1962e-03  2.4714e-02
δ Gimp : 3.1140e-03
δ G0   : 9.0832e-05
δ Σ    : 4.8577e+00
Impurity 3:
δn imp : 6.4522e-02
δn orb : 4.0829e-02  3.2435e-02  1.9490e-02  1.7823e-02  1.0409e-02
δ Gimp : 3.5310e-03
δ G0   : 5.3849e-05
δ Σ    : 7.3390e+00
============================================================

I would appreciate any suggestions on which technical choices (interaction form, basis rotation, DC, mixing strategy, temperature, etc.)
are most critical to obtain the metallic solution reported in the paper.

[aichhorn]

Hi,
Before looking into this in more detail: Have you contacted the authors of the mentioned paper, in particular first author Banerjee for the calculations details? They were using TRIQS, too, so it should be not so difficult to reproduce exactly what they did with their input. Everything else here is painful guessing.

[the-hampel]

Hi,
I agree to what @aichhorn wrote. I only had a quick look and I would like to note:

1. you did perform a para-magnetic calculation and did not allow for magnetic moments to form, whereas the paper you cite in Fig 3 shows magnetic states!
2. temperature: you use beta=40 whereas in the paper other temperatures are used for DMFT.
3. the QP peaks at the fermi level in the paper are rather small / narrow. Maybe G(beta/2) is not reliable here.

Best,
Alex

[mlei012]

Hi Markus @aichhorn and Alex,

Thank you so much for your reply. I just reached out to the author for clarification on this point.

I am guessing Banerjee used wien2k + TRIQS/DFTTools, and the projection window is −2 eV to +3 eV relative to the Fermi energy. I am not sure weather the projection window is the reason.

When I tried wien2k + solid_dmft, it always says

Largest imaginary element of delta(infty) e.g. of the local part of G0: 0.639821, is larger than the set parameter imag_threshold 1e-05

I find the Rotation matrices have large imaginary part.

Rotation matrices
rot_mat[ 0]                   real part                                    imaginary part
            -0.50000  0.86603  0.00000 -0.00000  0.00000    0.00000  0.00000 -0.00000  0.00000 -0.00000
            -0.86603 -0.50000  0.00000 -0.00000  0.00000    0.00000  0.00000  0.00000  0.00000 -0.00000
             0.00000  0.00000 -0.00000  0.00000  1.00000    0.00000  0.00000  0.00000  0.00000  0.00000
            -0.00000  0.00000  0.00000  0.00000  0.00000    0.00000  0.00000  1.00000  0.00000  0.00000
             0.00000  0.00000 -0.00000  0.00000  0.00000    0.00000 -0.00000  0.00000 -1.00000  0.00000

In the indmftpr file, I am using

cubic
0 0 2 0
0 0 0 0
0

for Mn,

complex
0 1 0 0
0 0 0 0

for O, and

complex
0 0 0 0
0 0 0 0

for Li.

Regarding the comments from Alex:

1. The Fig 3 also shows the paramagnetic spectral function (far-right panel).
2. Fig 4 shows the results at different temperatures, and all are metals.

Thanks again for your help.

Best,
Ming

[the-hampel]

Hi Ming,

ah sorry I missed those figures. Indeed they all look very metallic. Did you check that your wannier90 model density of states matches your DFT one?

One thing I do notice is that you maybe should specify the orbital order in solid_dmft. Since you are dealing with the full d-shell you should specify that your orbitals are ordered in W90 fashion (I assume). To do so please specify in the general section

h_int_basis = 'wannier90'

But this probably will not have such drastic effect. But otherwise the interaction terms are not correct.

Best,
Alex

[aichhorn]

Hi Ming,
I was just talking to Hrishit Banerjee. First of all, I think you can figure all this out most efficiently with him directly, since there are some details in theses calculations. For instance, he was using rotations to local frameworks and full rotational Kanamori Hamiltonians in that framwork (not sure if there were off-diagonals included then). Also, the supercell calculations should give you already some non-integer filling in the Mn atoms, since Li deficiency introduces doping in the Mn system. This doping should lead to metallic solutions - unless you get charge disproportionation between Mn sites. And they are using some other iteration scheme for the multiimpurity problem, which I do not understand right away, but it is not what solid DMFT is doing. All these details you can figure out most easily with him directly. Best, Markus

[mlei012]

Hi Markus and Alex,

Thank you so so much for your help. I talked with Hrishit yesterday, and I am now testing my own codes with Kanamori Hamiltonian.

I really enjoy using solid DMFT, since it is reliable and I don't need to debug by myself. BTW, does solid DMFT support wien2k + dmftproj workflow? Also I found it does not support h_int_type = kanamori_den_den

Best,
Ming

[the-hampel]

Hi Ming,

h_int_type = kanamori_den_den is only available on the unstable branch. It will be part of the next release. However, I must warn that the full 5d orbitals are not supposed to be used with a Kanamori Hamiltonian, or let's say it is not physical. If it is done it should be mentioned very clearly, but if the authors of the paper did so, it is of course worth trying to reproduce results. Did you try already with the corrected orbital order?

But I must also concur with what Markus wrote. You clearly have some integer filling in your impurities. If the authors of the paper constructed the orbitals differently leading to fractional occupations an insulating state is much harder to get. So this should be carefully cross-checked, i.e. just compare the impurity occupations without dmft self-energy would be good to compare.

Currently, we do not support a wien2k + dmtproj workflow. However, if you follow the dfttools tutorials to run wien2k + dmftproj + converter you can use the resulting h5 archive with solid_dmft without problems. Only the charge self-consistent calculations are not possible currently. All other things should work if the hdf5 archive is created with dfttools. That was the idea of solid_dmft: any h5 archive created by dfttools converters, no matter which code, will work.

Best,
Alex

[mlei012]

Hi Alex,

Thank you for the explanation! I just tried with h_int_basis = 'wannier90', and it still goes to an insulating state. I am now testing my own code.

Best,
Ming