# The SU(N) Heisenberg model of quantum permutations

Frederic Mila, Ecole Polytechnique Federale de Lausanne

12.06.2015 at 09:00

The interest in the SU(N) Heisenberg model has dramatically raised recently due to the possibility to realize it experimentally in the context of ultra-cold, multi-color fermionic atoms in optical lattices. 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 diagonalizations 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.

A 449 - Theresienstr. 37