The study of interacting topological bands with a tunable bandwidth offers a unique platform to study the interplay of intertwined orders and emergent non-electronic excitations. Here we design a time-reversal symmetric and sign-problem-free electronic model with tunable Chern bands carrying valley-contrasting Chern number, interacting via competing (anti-)ferromagnetic interactions. Using numerically exact quantum Monte-Carlo computations, we analyze the many-body phase-diagram as a function of temperature and band filling fractions over a wide range of electronic bandwidth, interaction anisotropy, and an Ising spin-orbit coupling. At a commensurate filling of the Chern bands, the ground state hosts intra-valley ferromagnetic coherence and inter-valley antiferomagnetism, thus realizing an insulating Chern antiferromagnet (CAF). Upon doping, the ground-state develops superconductivity, but where the low-energy charged quasiparticles are composite objects -- electrons dressed by multiple spin-flip excitations. These spin-polaron (or skyrmion) excitations persist in the presence of a weak spin-orbit coupling. In a companion article, we address the emergent symmetries and low-energy field-theoretic aspects of the problem and reveal the proximity to a deconfined quantum critical point. We end by providing a general outlook towards building microscopic connections with models of interacting moiré materials, including twisted bilayer graphene, where many of the ingredients considered here are naturally present.
Wang et al. (Wed,) studied this question.