How is the Hamiltonian saved in the SIESTA code?
The Hamiltonian is saved for the real space orbital connections, i.e., it is saved as a sparse matrix with supercell elements that describe the Hamiltonian elements between the two orbitals.
The Hamiltonian and overlap matrices are saved in either: <systemlabel>.HS or the <systemlabel>.HSX file.
For some details, you can look in the code: m_hs_matrix.F90 which has some descriptions that may be useful.