# Fermionic systems

```{toctree}
:maxdepth: 1

hubbard_dimer
hubbard_chain
extended_hubbard_chain
spin_exchange
flux_threaded_ring
```

The sequence moves from a solvable Hubbard bond to collective correlations on finite rings, competing order in the extended Hubbard model, a symmetry-constrained spin sector, and flux response in a complex Hermitian Hamiltonian.