The SU(N) Heisenberg Model of Quantum Permutations

<strong>Seminar of the School of Physical Sciences -----------------------------------------------------------</strong> Title: <strong>The SU(N) Heisenberg Model of Quantum Permutations</strong> Speaker: <strong>Frédéric Mila</strong> (Ecole Polytechnique Fédéral de Lausanne) Date: <strong>February 18, 2015 (Wednesday)</strong> <strong>Abstract: </strong>The interest in the SU(N) Heisenberg model has dramatically risen recently due to the possibility to realize it experimentally in the context of ultra-cold, multi-color fermionic atoms in optical lattices. For the fundamental irreducible representation, this model simply describes quantum permutations between N-flavor objects on a lattice, the same way as the spin-1/2 Heisenberg model describes permutations between up and down spins. In this talk, after a brief review of its basic properties and of some exact results in 1D, I will discuss the phases that have been identified so far in 2D and for intermediate values of N (typically N=2 and 3), which range from long-range or algebraic color order to the spontaneous formation of singlet plaquettes. Then, I will discuss the more difficult case of larger values of N, for which exact diagonalization could only be performed very recently thanks to the implementation of advanced properties of the permutation group. Finally, I will briefly discuss the case of higher irreducible representations, for which more exotic ground states such as chiral liquids have been proposed.