EFFECTIVE LATTICE MODELS FOR TWO-DIMENSIONAL QUANTUM ANTIFERROMAGNETS

We introduce a 2+1 dimensional lattice model, S0, of N complex scalars coupled to a compact U(1) gauge field as a description of quantum fluctuations in SU(N) antiferromagnets. Duality maps are used to obtain a single effective action for the Néel and spin-Peierls order parameters. We examine the phases of S0 as a function of N: the N→∞ limit can be deduced from previous work. At N=1, S0 describes monopoles and their Berry phases, spin-Peierls order, but not the Néel field: Monte-Carlo simulations show a second-order transition from a spin-Peierls phase to a Higgs phase which is the remnant of the Néel phase.