Hubbard chains: finite ground states and spin-charge excitations¶
All models · Half-filled tutorial · Doped tutorial
Hubbard calculations have separate charge momenta and spin rapidities. A finite ground state, a thermodynamic elementary dispersion and a two-particle continuum edge are distinct outputs, with different restrictions.
| What to calculate | Program | Coverage and guide |
|---|---|---|
| Finite periodic ground states | bethe-hubbard-pbc |
Periodic Hubbard: repulsive half filling, balanced attraction and selected doped shells on even rings; unrestricted free limit |
| Finite free-end ground states | bethe-hubbard-obc |
Open Hubbard: all physical fillings/spin projections, either interaction sign and either length parity |
| Half-filled spinon, holon and antiholon lines | bethe-hubbard-dispersion |
Half-filled dispersions, U>0 and zero field |
| Doped spinon and charge lines | bethe-hubbard-dispersion |
Doped dispersions, U>0 and zero field |
| Half-filled two-particle continuum edges | bethe-hubbard-continuum |
Continuum guide: spinon pairs and charge-containing families |
Match the Hamiltonian and energy reference¶
Finite-system tools use hopping \(t=1\) and the unshifted interaction \(U n_{\mathrm{up}}n_{\mathrm{down}}\). The dispersion tool defaults to the symmetric interaction convention, useful for SO(4) formulations. Particle-changing excitations also require a choice of Hamiltonian or Fermi-level energy reference. The tutorials show these shifts explicitly; matching the ground-state energy alone does not fix a particle-addition/removal dispersion convention.
The sector note explains finite periodic branch restrictions. Open-chain symmetry mappings can solve an auxiliary sector; interpret its roots together with the mapping flags and energy offset in the physical result.
From elementary lines to continuum edges¶
The continuum solver combines constituent dispersions and optimizes at fixed total momentum. It gives family boundaries, not spectral weights. The charge-continuum method note documents conventions, extrema searches and numerical budgets behind those calculations. Quadrature, momentum inversion and extrema convergence are separate from the number of arithmetic bits.