  We compute the electronic structure of acceptor clusters in silicon by using
three methods to include electron correlations: the full configuration
interaction, the Heitler-London approximation, and the unrestricted
Hartree-Fock method. We show both the HL approach and the UHF method are good
approximations to the ground state of the full CI calculation for a pair of
acceptors and for finite linear chains. The total energies for finite linear
chains show the formation of a 4-fold degenerate ground state when there is a
weak bond at the end of the chain, which is shown to be a manifold of
topological edge states. We identify a change in the angular momentum
composition of the ground state at a critical pattern of bond lengths and show
it is related to a crossing in the Fock matrix eigenvalues. We also test the
symmetry of the UHF solution and compare it to the full CI; the symmetry is
broken under almost all the arrangements by the formation of a magnetic state
in UHF, and we find further broken symmetries for some particular arrangements
related to crossings or potential crossings between the Fock-matrix
eigenvalues. We also compute the charge distributions across the acceptors
obtained from the eigenvectors of the Fock matrix: with weak bonds at the chain
ends, two holes are localized at either end of the chain while the others have
a nearly uniform distribution over the middle; this implies the existence of
the non-trivial edge states. We apply the UHF method to treat an infinite
linear chain with periodic boundary conditions. We find the band structures in
the UHF approximation and compute the Zak phases for the occupied Fock-matrix
eigenvalues; we find they do not correctly predict the topological edge states
in this interacting system. We find direct study of the quantum numbers
characterising the edge states provides a better insight into their topological
nature.
