  The interplay between many-body interactions and the kinetic energy gives
rise to rich phase diagrams hosting, among others, interaction-induced
topological phases. These phases are characterized by both a local order
parameter and a global topological invariant, and can exhibit exotic ground
states such as self-trapped polarons and interaction-induced edge states. In
this work, we investigate a realistic scenario for the quantum simulation of
such systems using cold Rydberg-dressed atoms in optical lattices. We consider
spinless fermions on a checkerboard lattice, interacting via the tunable-range
effective potential induced by the Rydberg dressing. We perform a detailed
analysis of the phase diagram at half- and incommensurate fillings, in the
mean-field approximation. We furthermore study the stability of the phases with
respect to temperature within the mean-field approximation and with respect to
quantum fluctuations using the density matrix renormalization group method.
Finally, we propose an implementation protocol, and in particular identify
attainable regimes of experimental parameters in which the topological
properties of the model become accessible. Our work, thereby, opens a realistic
pathway to the outstanding experimental observation of this predicted phase in
state-of-the-art cold atom quantum simulators.
