Access to Hamiltonian or Density Matrix

[NasiLemak]

I wonder if there is any method that the users of ATK can access or export Hamiltonian / Density Matrix so that they can do some other analysis of the system.
Hopefully ATK developer can give a positive answer.
Thank you so much.

[Nordland]

I should be able to help you, but first you must give me a little more information.

What kind of configurations is it for?

[NasiLemak]

Thank you so much.
What I want to do is to extract the density matrix or Hamiltonian so that I can calculate some other physical properties.
First, I want to try a bulk configuration, and further more, if possible, I also want to try the scattering region of a device configuration.

[Nordland]

I have cooked up a little code snippet that should get the job done for all your needs.

Code: python

def extractHamiltonianAndOverlap(configuration, kx=0.0, ky=0.0, kz=0.0):
    """
    Routine for getting the hamiltonian and overlap for a given k-point.
    """
    from NL.ComputerScienceUtilities.Functions import realMatrixToNumpy
    # Get the density matrix calculator.
    dmc = configuration.calculator()._densityMatrixCalculator()
    # Get the neighbourlist.
    nb = dmc.neighbourlist()
    # Calculate the phases for this k-point.
    phases = nb.calculatePhases(NLEngine.Cartesian3D(kx,ky,kz))
    # Get a reference for the sparse data structure.
    sparse_H = dmc.hamiltonian()
    sparse_S = dmc.overlap()
    # Perform the fourierTransform to get the dense representation.
    # Change to NLEngine.DOWNDOWN to get spin down.
    spin = NLEngine.UPUP
    denseS = NLEngine.fourierTransform(sparse_S.getSparseCSR(spin), phases)
    denseH = NLEngine.fourierTransform(sparse_H.getSparseCSR(spin), phases)
    # Convert to numpy for easy use in Python.
    real_numpy_S = realMatrixToNumpy(NLEngine.realPart(denseS))
    imag_numpy_S = realMatrixToNumpy(NLEngine.imaginaryPart(denseS))
    real_numpy_H = realMatrixToNumpy(NLEngine.realPart(denseH))
    imag_numpy_H = realMatrixToNumpy(NLEngine.imaginaryPart(denseH))
    # Construct complex numpy.
    H = real_numpy_H + complex(0.0,1.0)*imag_numpy_H
    S = real_numpy_S + complex(0.0,1.0)*imag_numpy_S
    # Return
    return H,S

It is not sure that this exacted snippet will work forever, but it is likely. An example of the usage:

Code: python

H, S = extractHamiltonianAndOverlap(bulk_configuration, kx=0.0, ky=0.5, kz=0.2)
print H
print S

I hope it helps your forward.

[NasiLemak]

Thank you so much. That is what I want. I will try that later.

[zhangguangping]

I have cooked up a little code snippet that should get the job done for all your needs.
I hope it helps your forward.

Dear Nordland,
From your code. I see, you just move the interactions the unitcell with the neighborings into the unitcell with multiplying the phase,then we have a N*N dimension of H and S,where  N is the dimension of the unit cell. If we want to get the bandstructure, we should construct the H and S like this for every k points and then solve the equation ES{Φ}=H{Φ}? In which {Φ} is expanded in the basis orbits in the unit cell.

Thanks for your answer in advance.

[Nordland]

Exactly. Well spotted!

If you only are after calculating the band-structure, I would recommend that you use the build-in routine for it
since it will be done in native C++ rather than in Python.

[NasiLemak]

I would like to point out one small typo in line 19. This line is for H but not S, thus the "sparse_S" should be "sparse_H"。
After correct this typo, the script can do the extraction of H and S exactly.

Thank you so much!

[Nordland]

Good spotted.

I have updated the script above for future users.

[davalenciah]

thanks for the code, but
when I used its
I got

Hamiltonian =
[[ -1.79177926e-01+0.j   4.31381157e-04+0.j   7.47164661e-04+0.j ...,
    1.58944871e-02+0.j   1.67094370e-06+0.j  -2.75295477e-02+0.j]
 [  0.00000000e+00+0.j   4.49252502e-03+0.j  -9.36283703e-04+0.j ...,
    2.22503996e-05+0.j  -4.14151484e-07+0.j   1.12248995e-05+0.j]
 [  0.00000000e+00+0.j   0.00000000e+00+0.j   3.41157733e-03+0.j ...,
    5.75047611e-07+0.j   9.49960993e-04+0.j  -2.47628152e-06+0.j]
 ...,
 [  0.00000000e+00+0.j   0.00000000e+00+0.j   0.00000000e+00+0.j ...,
    7.31291547e-01+0.j   1.20404864e-06+0.j   4.20901658e-03+0.j]
 [  0.00000000e+00+0.j   0.00000000e+00+0.j   0.00000000e+00+0.j ...,
    0.00000000e+00+0.j   9.79341845e-01+0.j  -1.15453173e-05+0.j]
 [  0.00000000e+00+0.j   0.00000000e+00+0.j   0.00000000e+00+0.j ...,
    0.00000000e+00+0.j   0.00000000e+00+0.j   7.29846714e-01+0.j]]

I would like to get the complete Hamiltonian and overlap not just a part.
How can I get the complete matrix

Thanks

[Anders Blom]

The objects H and S do contain the full Hamiltonian/overlap matrices. It's only when numpy prints them, in the default format, to the terminal that it shortens the output, so you don't get 100,000 lines of text output.

[davalenciah]

thanks

how could I change the default print i numpy to see
all elemnet of matrix H?

[Anders Blom]

Hmm, you should keep in mind this is potentially a very large matrix. I'm not sure that printing it to the screen is very helpful. You can either do

Code: python

for i in range(X.shape[0]):
    for j in range(X.shape[1]):
        print X[i,j],
    print

or simpler

Code: python

numpy.set_printoptions(threshold='nan')
print X

However in this case you get the braces [ and ] too. And do pipe the output to a file!

[davalenciah]

Thanks for all replies 

I was wondering if the units of Hamiltonian elements
are eV, Hartree or another one?

[Anders Blom]

All internal quantities in ATK are typically in Hartree and Bohr or combinations thereof.