Abstract
We investigate the effects of atomic interaction and artificial gauge potential in a quantum simulation of classical magnetism via ultracold bosonic atoms in triple wells. The system can be mapped into a transverse-field spin chain with Ising interaction under a twisted boundary condition. It undergoes a phase transition from planar to three-dimensional spin configurations, similar to the para-to-antiferromagnetic phase transition in the transverse-field Ising model, and the artificial gauge potential can tune this phase transition. The phase diagram is obtained, including ferromagnetic and spiral phases, similar to those simulated in Struck et al. [Struck, \"Olschl\"ager, Targat, Soltan-Panahi, Eckardt, Lewenstein, Windpassinger, and Sengstock, Science 333, 996 (2011)].
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