New states of matter in one- and twodimensional lattice models

In the first part, we consider a system of neutral, bosonic atoms on a square lattice subject to an artificial magnetic field. We focus on a field strength of half a Dirac flux quantum through every plaquette. We point out that this system exhibits not only superfluid order but also antiferromagnetic order. In the second part, we consider SU(N) spin chains and present an approach to generalize Haldane\u27s conjecture for abritrary spin representations