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The interplay between many-body interactions and the kinetic energy givesrise to rich phase diagrams hosting, among others, interaction-inducedtopological phases. These phases are characterized by both a local orderparameter and a global topological invariant, and can exhibit exotic groundstates such as self-trapped polarons and interaction-induced edge states. Inthis work, we investigate a realistic scenario for the quantum simulation ofsuch systems using cold Rydberg-dressed atoms in optical lattices. We considerspinless fermions on a checkerboard lattice, interacting via the tunable-rangeeffective potential induced by the Rydberg dressing. We perform a detailedanalysis of the phase diagram at half- and incommensurate fillings, in themean-field approximation. We furthermore study the stability of the phases withrespect to temperature within the mean-field approximation and with respect toquantum fluctuations using the density matrix renormalization group method.Finally, we propose an implementation protocol, and in particular identifyattainable regimes of experimental parameters in which the topologicalproperties of the model become accessible. Our work, thereby, opens a realisticpathway to the outstanding experimental observation of this predicted phase instate-of-the-art cold atom quantum simulators.

Accessing the topological Mott insulator in cold atom quantum simulators with realistic Rydberg dressing