Topological aspects of SU(N) magnetism and its cold atom realization
Thomas Quella, Universität Köln
SU(N) spin systems exhibit a number of novel topological quantum states, including specifically a variety of Haldane phases (in 1D) and abelian and non-abelian spin liquid phases (in 2D). In this talk we will review the classification of Haldane phases and their characterization in terms of fractionalized boundary spins and non-local string order parameters. Moreover, we will address the possible realization of these phases in ultra-cold gases of alkaline-earth fermions. If time permits we will also briefly comment on the systematic design of critical and topological long-range SU(N) spin models in one and two dimensions which are based on infinite dimensional matrix product states associated with SU(N) WZW models.