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This PR adds a tutorial where I build and analyze a Picket-Fence (comb-like) Hamiltonian using the ModelHamiltonian package.
The idea was to create something that not only shows how to generate integrals, but also how to go from a custom topology → Hamiltonian → actual physical insights.
What’s in the tutorial
Constructing the picket-fence connectivity matrix
Generating 0-, 1-, and 2-body integrals
Solving the system using PySCF FCI (fci.direct_spin1)
Converting to chemist notation and checking consistency
Verifying that the Hamiltonian matches the expected structure
Comparing energies across formulations (FCI / reduced / geminal)
Plotting ground state energy vs coupling
A small localization analysis using IPR from the RDMs
Saving outputs to .npz and .fcidump
Notes
Everything is tested at half-filling, and the energy checks are consistent across methods.
Happy to improve or restructure based on feedback 🙂