Unconventional quantum phases in quantum magnetism and cold atoms
Prof. Frédéric Mila (École Polytechnique Fédérale de Lausanne, Switzerland)

The search for new quantum phases with original properties is one of the major themes in quantum many-body physics. Quantum magnets are a major player in the field, with the prediction of several types of new phases such as nematic phases or quantum spin liquids of various types. The major challenge at the moment is to find good experimental realizations of these phases in the context of quantum magnets. In this talk, starting from the observation that SU(N) Heisenberg models, that have already been investigated in the context of quantum magnetism for N=3 and 4 for some time, can also be realized in the context of cold fermions, I will report on recent progress made recently on these models on various lattices, with emphasis on two results: the stripe-like, three-sublattice flavour order stabilized on the square lattice, and the peculiar case of SU(4) on the same lattice, where a spontaneous dimerization takes places, followed by a Néel ordering of the remaining 6-dimensional local degrees of freedom.