Nonlinear sigma models and quantum spin systems

Microscopic models of quantum antiferromagnets are investigated on the basis of a mapping onto effective low-energy Hamiltonians. Lattice effects are carefully taken into account and their role is discussed. We show that the presence of an external staggered magnetic field modifies in a nontrivial way the usual mapping onto the nonlinear sigma model, leading to the appearance of terms neglected in previous works. Our analysis is compared with Lanczos diagonalizations of S51 Heisenberg chains in a staggered field, confirming the validity of the single-mode approximation for the evaluation of the dynamical structure factor. The results are relevant for the interpretation of experiments in quasi-one-dimensional compounds. Microscopic realizations of SU~4! spin chains are also discussed in the framework of spin-orbital lattice systems. The low-energy physics is shown to be described by sigma models with topological angle u in one dimension. This mapping strongly suggests that the one-dimensional CP3 model ~with u5p) undergoes a second-order phase transition as a function of the coupling.