  Topology in quantum many-body systems has profoundly changed our
understanding of quantum phases of matter. The paradigmatic model that has
played an instrumental role in elucidating these effects is the
antiferromagnetic spin-1 Haldane chain. Its ground state is a disordered state,
with symmetry-protected fourfold-degenerate edge states due to fractional spin
excitations. In the bulk, it is characterised by vanishing two-point spin
correlations, gapped excitations, and a characteristic non-local order
parameter. More recently it was understood that the Haldane chain forms a
specific example of a more general classification scheme of symmetry protected
topological (SPT) phases of matter that is based on ideas connecting to quantum
information and entanglement. Here, we realise such a topological Haldane phase
with Fermi-Hubbard ladders in an ultracold-atom quantum simulator. We directly
reveal both edge and bulk properties of the system through the use of
single-site and particle-resolved measurements as well as non-local correlation
functions. Continuously changing the Hubbard interaction strength of the system
allows us to investigate the robustness of the phase to charge (density)
fluctuations far from the regime of the Heisenberg model employing a novel
correlator.
