Classification of nematic order in 2+1D: Dislocation melting and $O(2)/Z_N$ lattice gauge theory

Abstract

Nematic phases, 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 $C_N$ in 2+1D. Starting from the space groups of underlying $2d$ crystals, we present a general classification scheme incorporating $C_N$ nematic phases that arise from dislocation-mediated melting and discuss the conventional tensor order parameters. By coupling the $O(2)$ matter fields to the $Z_N$ lattice gauge theory, an unified $O(2)/Z_N$ lattice gauge theory is constructed in order to describe all these nematic phases. This lattice gauge theory is shown to reproduce the $C_N$ nematic-isotropic liquid phase transitions and contains an additional deconfined phase. Finally, using our $O(2)/Z_N$ gauge theory framework, we discuss phase transitions between different $C_N$ nematics.

20 pages, 7 figures, 1 table

References in corpus (10)

• "Deconfined" quantum critical points
• Theory of Electron Nematic Order in LaOFeAs
• Electronic liquid crystal state in the high-temperature superconductor YBCO(6.45)
• Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
• Diagnosing Deconfinement and Topological Order
• Experimental observables near a nematic quantum critical point in the pnictide and cuprate superconductors
• Stripe melting and quantum criticality in correlated metals
• Tendencies toward nematic order in YBa2Cu3O6+x: Uniform distortion vs. incipient charge stripes
• The quantum smectic as a dislocation Higgs phase
• Model of Fractionalization of Faraday Lines in Compact Electrodynamics

Cited by in corpus (3)

• Liquid Crystal Distortions Revealed by an Octupolar Tensor
• Generic first-order phase transitions between isotropic and orientational phases with polyhedral symmetries
• The symmetries of octupolar tensors