Chiral phases and Landau-forbidden transitions in one dimension

Abstract

The common lore in statistical physics suggests that phases and transitions of matter are generally classified by what is called the Landau-Ginzburg-Wilson paradigm. In two dimensions, however, quantum models can exhibit “deconfined” continuous transitions between ordered phases, which are forbidden by the Landau classification. On this thesis, we introduce a one-dimensional quantum spin model with three ordered phases: A chiral spin state, where the system orders into three-spin “fluxes”, an antiferromagnetic state, and a novel phase which we denote as the Klein paramagnet. We find that all transitions from the chiral phase are continuous and beyond the Landau paradigm.