[Seminar] "The ground states of two-dimensional SU(N) Heisenberg models" by Prof. Karlo Penc

The low energy physics of the Mott insulator with spin and orbital degrees of freedom in transition metal compounds and ultracold fermionic atoms on optical lattices is described by SU(N) symmetric Heisenberg model, where the states of the N-dimensional local Hilbert space are exchanged on the neighboring sites. The quantum fluctuations in these models are enhanced compared to usual magnetic system, and depending on the lattice geometry,  ordered as well as disordered phases of different kind can be realized. I will start with the simplest examples for ordered states in the SU(3) model on the triangular and square lattice, the latter being selected by quantum fluctuations.  Considering larger N, the SU(4) Heisenberg model undergoes a spontaneous dimerization on the square lattice, and is quantum liquid with algebraic spin correlation on the honeycomb lattice. Finally, in some cases a chiral phase is realized. I will discuss the general principles behind the selection of different ground states.