Motivated by recent advances in fabricating artificial lattices in
semiconductors and their promise for quantum simulation of topological
materials, we study the one-dimensional dimerized Fermi-Hubbard model. We show
how the topological phases at half-filling can be characterized by a reduced
Zak phase defined based on the reduced density matrix of each spin subsystem.
Signatures of bulk-boundary correspondence are observed in the triplon
excitation of the bulk and the edge states of uncoupled spins at the
boundaries. At quarter-filling we show that owing to the presence of the
Hubbard interaction the system can undergo a transition to the topological
ground state of the non-interacting Su-Schrieffer-Heeger model with the
application of a moderate-strength external magnetic field. We propose a robust
experimental realization with a chain of dopant atoms in silicon or
gate-defined quantum dots in GaAs where the transition can be probed by
measuring the tunneling current through the many-body state of the chain.Comment: 11 pages, 7 figure
