Auto chemical potential adjustment

[EndsonLana]

Summary

An auto process for the chemical potential to adjust dynamically to the fixed particle number.

Motivation

The chemical potential adjustment methods I found seems to require a lot of extra loops, but the problems like OSMP(Orbital Selective Mott Phase) requires a dynamically adjusting chemical potential to keep the particle numbers. For example, for a Jahn-Teller effect system, the total number of electrons N of 3 t2g orbitals is set to 4.

Implementation

I wonder if there is some quick way like a snippet of python scripts to do this? Or perhaps a particle number parameter in Solver.solve()?

Formatting

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[the-hampel]

Hi @EndsonLana, I am not sure I understand 100% what you mean. Currently, you would always write a little function that computes the density on the lattice Gf, i.e.:

F_optimize(mu):
    mpi.report("Trying out mu = {}".format(str(mu)))
    calc_dens = calc_lattice_density(your function) - target_density
    mpi.report(f"Target density = {target_density}; Delta to target = {calc_dens}")
    return calc_dens

and then use either the triqs interal dichotomy method (might take long): https://triqs.github.io/triqs/unstable/documentation/python_api/triqs.utility.dichotomy.dichotomy.html and pass the function F_optimize as first argument, or you can use one of the scipty optimizers. For example in triqs/dft_tools we are using Newton as optimizer:

from scipy.optimize import minimize, newton, brenth
chemical_potential = newton(func=F_optimize,
                                             x0=mu_guess,
                                             tol=precision, maxiter=max_loops,
                                             )

This would be done in each DMFT loop. We do not provide a function in the solver to perform the chemical potential finding. You can take a look on how this is implemented in triqs/dft_tools here: https://github.com/TRIQS/dft_tools/blob/b87ca75c89e1b0f0189807747f0b02f71d366141/python/triqs_dft_tools/sumk_dft.py#L1944

Let me know if you have further questions.

Best, Alex

[EndsonLana]

Dear Dr.Hampel, This is exactly what I am looking for. My question is that in a model Hamiltonian, the density computation is hard to achieve when I am using imaginary frequency in triqs. Therefore the chemical potential is hard to get. Sincerely, E.L.

[Wentzell]

@EndsonLana Has the point been clarified for you? If so please close the issue.