Classification of nematic order in 2+1 dimensions: Dislocation melting and O (2)/ ZN lattice gauge theory

Abstract

Nematicphases, breaking spontaneously rotational symmetry, provide for ubiquitously observed states of matter in both classical and quantum systems. These nematic states may be further classified by their N-fold rotational invariance described by cyclic groups CN in 2+1D. Starting from the space groups of underlying 2D crystals, we present a general classification scheme incorporating CN nematic phases that arise from dislocation-mediated melting and discuss the conventional tensor order parameters. By coupling the O(2) matter fields to the ZN lattice gauge theory, a unified O(2)/ZN lattice gauge theory is constructed in order to describe all these nematic phases. This lattice gauge theory is shown to reproduce the CN nematic-isotropic liquid phase transitions and contains an additional deconfined phase. Finally, using our O(2)/ZN gauge-theory framework, we discuss phase transitions between different CN nematics.