Trace of the density matrix is 1.00018 instead of 1

Dear all,

I have an issue, where I couldn't find any helpful hint or solution so far. I am using Triqs dft tools for the material FeSe (5-orbital Kanamori interaction). We obtained the DFT input with Wannier90 using two different functionals PBE and HSE. With HSE ( I have no problems at any temperature from beta=50-150 and different interactions the code works well and converges nicely). However when I use the DFT output computed using PBE I get this error message in a beta range from 50 to 80 but not at beta 100 and 150. I tried many things to fix it, but this error always occurs and I don't understand it properly. The error occurs at a seemingly random iteration for example at iteration 5 or 3 or 2 or 7 and the value of the trace of density matrix changes also. The error I obtain is:

S.solve(h_int=h_int, p) File "/obs/kbaumann/triqs_install/lib/python3.9/site-packages/triqs_cthyb/solver.py", line 140, in solve solve_status = SolverCore.solve(self, params_kw) RuntimeError: .. Error occurred at Tue Mar 30 19:29:37 2021

.. Error .. calling C++ overload .. solve() -> void .. in implementation of method SolverCore.solve .. C++ error was : .. Triqs runtime error at /obs/kbaumann/triqs_install/cthyb.src/c++/triqs_cthyb/measures/density_matrix.cpp : 66

Trace of the density matrix is 1.00018 instead of 1 .. Error occurred on node 0

I would be grateful for any hint how to fix it. Maybe it is an obvious issue, but I don't understand it.

Best regards,

Karla Baumann

Hi @karlabaumann,

I indeed observed that the trace of rho can deviate a bit from 1 in a few calculations. In principle this should not happen, unless your QMC sampling has problems. The probability of all impurity states is normed to 1, as it should in a proper density matrix. I usually only get a warning:

Warning :: Trace of the density matrix is 0.9999999999999 instead of 1

Hence, the deviation that I see is very very small. I think it makes sense that cthyb stops if the deviation gets too large (check https://github.com/TRIQS/cthyb/blob/95d4a58c034e50a87bda0b421b335de0065f32e9/c%2B%2B/triqs_cthyb/measures/density_matrix.cpp#L66 for more information on the exact threshold). I am not 100% sure where this deviations are stemming from, but here some ideas for where to start:

Can you check if you see such warning already earlier in your error output and see if it grows?
In general does the iteration run smoothly with measure_density_matrix = False ? Good sign?
Can you also check if your calculations at these specific temperatures have small off-diagonal terms in your local Hamiltonian, that cthyb reports just before solving.
Is there a warning that that the tail-fit fails just before solving the impurity problem? Maybe cthyb has problems for some of the temperatures to properly extract the hybridization from G0_iw (make sure that there are always enough Matsubara frequencies so that G0_iw decays properly to a constant value at large omega_n for all beta).
carefully check that your wannier90 input hamiltonian is real, if there are small complex parts cthyb maybe does not properly detect them and has problems with dealing with them

Maybe @krivenko has some further ideas, as he implemented the routine into the solver if I remember correctly.

Hi Alexander Hampel,

many many thanks for your detailed and fast reply!

I checked all the points on your list and luckily I could fix the issue. I had now one converged run with the PBE functional at beta=50. Indeed it was, as you suggested, related to the tail fit. So I still get a warning but the code doesn't stop. And also I checked the output files before and the error was growing.

These points on the list, did not apply to my problem:

small off-diagonal terms in your local Hamiltonian
wannier90 input hamiltonian has complex hopping terms

This point I didn't check so far:

"In general does the iteration run smoothly with. measure_density_matrix = False ? Good sign? "

but with adjusting the tail fit I managed to get the issue under control.

Many many thanks again!!!

Best regards,

Karla Baumnn

Le 2021-04-06 15:40, Alexander Hampel a écrit :

Hi @karlabaumann,

I indeed observed that the trace of rho can deviate a bit from 1 in a few calculations. In principle this should not happen, unless your QMC sampling has problems. The probability of all impurity states is normed to 1, as it should in a proper density matrix. I usually only get a warning:
Warning :: Trace of the density matrix is 0.9999999999999 instead of 1
Hence, the deviation that I see is very very small. I think it makes sense that cthyb stops if the deviation gets too large (check https://github.com/TRIQS/cthyb/blob/95d4a58c034e50a87bda0b421b335de0065f32e9/c%2B%2B/triqs_cthyb/measures/density_matrix.cpp#L66 for more information on the exact threshold). I am not 100% sure where this deviations are stemming from, but here some ideas for where to start:

Can you check if you see such warning already earlier in your error output and see if it grows?

In general does the iteration run smoothly with measure_density_matrix = False ? Good sign?

Can you also check if your calculations at these specific temperatures have small off-diagonal terms in your local Hamiltonian, that cthyb reports just before solving.

Is there a warning that that the tail-fit fails just before solving the impurity problem? Maybe cthyb has problems for some of the temperatures to properly extract the hybridization from G0_iw (make sure that there are always enough Matsubara frequencies so that G0_iw decays properly to a constant value at large omega_n for all beta).

carefully check that your wannier90 input hamiltonian is real, if there are small complex parts cthyb maybe does not properly detect them and has problems with dealing with them

Maybe @krivenko has some further ideas, as he implemented the routine into the solver if I remember correctly.

Hi Karla,

okay sounds good. If I understand you correctly you changed the tail fitting for the solver output right (the fitting that one specifies in the solve params)? This probably means, that after a few iterations the G0_iw that you give to the solver as input becomes ill-conditioned in some way, when using bad fitting parameters. Better keep an eye on that problem, and check also for convergence of the QMC sampling.

I will close the issue for now. Just open a new one and refer to this one, if the problem reappears.

Best, Alex

TRIQS / dft_tools

Trace of the density matrix is 1.00018 instead of 1 #168