Quantum simulations made easy plane

Abstract: 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.