  Ever since Heisenberg's proposal of a quantum-mechanical origin of
ferromagnetism in 1928, the spin model named after him has been central to
advances in magnetism, featuring in proposals of novel many-body states such as
antiferromagnets, emergent gauge fields in their confined (valence bond
crystal) and deconfined (resonating valence bond spin liquids) versions.
Between them, these cover much of our understanding of modern magnetism
specifically and topological states of matter in general. Many exciting
phenomena predicted theoretically still await experimental realisation, and
cold atomic systems hold the promise of acting as analogue 'quantum simulators'
of the relevant theoretical models, for which ingenious and intricate set-ups
have been proposed. Here, we identify a new class of particularly simple
quantum simulators exhibiting many such phenomena but obviating the need for
fine-tuning and for amplifying perturbatively weak superexchange or
longer-range interactions. Instead they require only moderate on-site
interactions on top of uncorrelated, one-body hopping--ingredients already
available with present experimental technology. Between them, they realise some
of the most interesting phenomena, such as emergent synthetic gauge fields,
resonating valence bond phases, and even the celebrated yet enigmatic spin
liquid phase of the kagome lattice.
