Effective field theory with a θ-vacua structure for two-dimensional spin systems

We construct a nonlinear sigma (NL sigma) model description of (2+1)-dimensional [(2+1)D] antiferromagnetic spin systems, by coupling together spin chains via interchain exchange terms. Our mapping incorporates methods developed recently by ourselves and by Senthil and Fisher, which aim at describing competition between antiferromagnetic and valence-bond-solid orders in quantum magnets. The resulting (2+1)D O(4) NL sigma model contains a topological theta term whose vacuum angle theta varies continuously with delta, the bond-alternation strength of the interchain interaction. This implies that the theta-vacua structure for this NL sigma model can be explored by tuning delta in a suitable 2D spin system, which is strongly reminiscent of the situation for 1+1 antiferromagnetic spin chains with bond alternation.