Quantum magnetism of ultracold atoms with a dynamical pseudospin degree of freedom

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We consider bosons in a Hubbard lattice with an $\text{SU}(\mathcal{N})$ pseudospin degree of freedom which is made dynamical via a coherent transfer term. It is shown that, in the basis which diagonalizes the pseudospin coupling, a generic hopping process affects the spin state, similarly to a spin-orbit coupling. This results, for the system in the Mott phase, in a ferromagnetic phase with a variable quantization axis. In extreme cases, it can even give rise to antiferromagnetic order.