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Heisenberg exchange coupling Jij(R=0)

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**Leonardo**:

Dear Colleagues,

I need your help in understanding an observation: Take any kind of small system (e.g. a small cluster of atoms or molecule). You can calculate the Hesienberg exchange coupling Jij(R) in two different ways: either as a "molecular configuration" or as a "bulk configuration" (using a large enough computational cell to avoid image interactions). For the latter, QATK together with your script "plot_Jij_vs_r.py" provides the coupling values Jij for R values corresponding to the interatomic distances. Doing exactly the same in the "molecular configuration" gives exactly the same Jij(R>0) values, BUT it gives an additional value for R=0! It turns out that Jij(R=0) is in general much stronger than all the other Jij values.

Could you please explain me the physical meaning for Jij(R=0)? Is it a measure for the coupling strength of two spins within the same atom? But why does this term not show up in the "bulk configuration" calculation?

With many sincere thanks for any hint in advance!

PS: The script "plot_Jij_vs_r.py" proposed in the QATK documentation is the same for QATK 2019 and the latest versions of QATK. However, this script provides much more convincing results when used to analyze the results obtained with the old QATK 2019 then with those given by QATK 2021. Is there a chance that the script "plot_Jij_vs_r.py" was not properly updated to reliably analyze the results given by the newer versions of QATK? Who is the author of "plot_Jij_vs_r.py"?

**Troels-Markussen**:

Hi,

The 'on-site' exchange parameter Jii should not be regarded as a physical result, but rather be ignored in the case of molecules, where it's currently calculated.

Concerning plotting of the Jij values I would recommend to use the build-in HeisenbergExchange analyzer available in QATK 2023.09. With this version I get the same results as shown in the tutorial about HeisenbergExchange http://docs.quantumatk.com/tutorials/heisenberg_exchange/heisenberg_exchange.html#id21 , also using the plot_Jij_vs_r.py script.

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