GitLab

Current status

• Vectorized low level systems store similar sites in SiteArrays, and similar terms of the Hamiltonian in syst.terms.
• With respect to translation symmetries, the data format of terms is correct (each term stores the associated symmetry element),
• Finalization uses site ordering enforced by the interface. This is impossible or hard to generalize symmetries that are more than 1D.
• When attaching a lead we compute the interface—sites that are connected to the lead by a hopping.
• A finalized system stores lead_interfaces—the indices of its low level sites that match the indices of the extra sites of the lead in the same order.

Goals

• We want to be able to finalize systems with ND translations, and therefore we won't be able to enforce a specific ordering on the sites.
• We still want to be able to attach the leads (duh).
• At this point we want to keep the logic of builder the same (attaching leads by flood fill).

Proposal

I think the apparent incompatibility between the goals is achieved by this format change:

Change lead_interfaces to be a mapping between the scattering region sites and the lead sites that only includes the sites that are connected by a hopping, instead of relying on the ordering of the sites in the infinite system.

Change lead_interfaces to be a 2D array of site numbers in the scattering region that correspond to specific sites in the lead unit cell upon translation by k symmetry vectors of the lead. In other words if interface[n, k] == i, that means that i'th site of the scattering region corresponds to the n'th site of the lead upon translation by k+1 lead symmetry vectors that aren't shared by the system. A value of -1 in the interface indicates that there is no site in the system that corresponds to the n'th site of the lead upon translation by k+1 lead symmetry vectors. Finally, interface.shape == (N_lead_sites, max_hopping_range).

1. This means that we finalize the systems without taking the interface into account (already a simplification), and have the same ordering of sites regardless of how the lead was attached.
2. When computing the new format for the lead_interfaces we only need a single lookup (something like searchsorted).
3. In principle this means that attaching a 2D lead to a 1D scattering region becomes legal (although we must specify which generator to use for the remaining 1D symmetry).