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RichRick1
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Apr 27, 2026
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I really like this tutorial! What I really like is that you compared results with original ones obtained from Richardson paper.
Looks good to merge!
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| The **Picket-Fence Model** is a special case of the Richardson-Gaudin model with equally spaced site energies and constant pairing interaction. | ||
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| It can be implemented by setting :math:`\mu_p = (p - \frac{N-1}{2}) + G` and :math:`J_{pq}^{\text{eq}} = G`. |
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I believe it should be only diagonal term of J_pq^{eq}. Should be fixed now
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The educational goal of this picket-fence tutorial is see how one can match the numerical benchmarks from Richardson (1966) paper (link in the notebook) with moha. This paper is as far as I understand one of the first ones in the field and I chose it because approximate methods like BCS are inaccurate for small system sizes, so it helps to have some pre-computed values. The code maps the pairing Hamiltonian to the library's spin-based HamRG class to get the one-body levels and interaction strengths right. We identify the states through their spin symmetry and occupation patterns, singlets for pair moves and triplets for single moves, while applying the energy shifts used in the original paper. The notebook now reproduces the values from Tables 1, 2, and 4 from the Richardson paper across the a range of coupling strengths, for N=4. Actually N=8 also works but requires more compute, I think it's best to keep it light for the tutorial. I've also attempted to integrate with the website, hope that works.