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.

arXiv comment20 pages, 7 figures, 1 table

References in corpus (49)

• Anyons in an exactly solved model and beyond
• "Deconfined" quantum critical points
• Electronic Liquid Crystal Phases of a Doped Mott Insulator
• Nematic order in iron superconductors - who is in the driver's seat?
• Nematic Fermi Fluids in Condensed Matter Physics
• Theory of Electron Nematic Order in LaOFeAs
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• Evidence for an Anisotropic State of Two-Dimensional Electrons in High Landau Levels
• Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states
• Divergent nematic susceptibility in an iron arsenide superconductor
• Electronic liquid crystal state in the high-temperature superconductor YBCO(6.45)
• Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
• Electrical Resistivity Anisotropy from Self-Organized One-Dimensionality in High-Temperature Superconductors
• Liquid Crystal Phases of Quantum Hall Systems
• Colloquium: Hidden Order, Superconductivity, and Magnetism -- The Unsolved Case of URu2Si2
• Superconductors are topologically ordered
• Spin Nematic Phase in S=1 Triangular Antiferromagnets
• Anisotropic States of Two-Dimensional Electron Systems in High Landau Levels: Effect of an In-Plane Magnetic Field
• Strongly Anisotropic Electronic Transport at Landau Level Filling Factor $\nu =9/2$ and $\nu =5/2$ Under Tilted Magnetic Field
• Competing orders in a magnetic field: spin and charge order in the cuprate superconductors
• Topological Defects Coupling Smectic Modulations to Intra-unit-cell Nematicity in Cuprate
• The Bond-Algebraic Approach to Dualities
• Signatures of Electronic Nematic Phase at Isotropic-Nematic Phase Transition
• Microscopic models for fractionalized phases in strongly correlated systems
• Universal Signatures of Fractionalized Quantum Critical Points
• Spin nematic state as a candidate of the hidden order phase of URu${}_2$Si${}_2$
• Deconfinement transition in three-dimensional compact U(1) gauge theories coupled to matter fields
• Duality in 2+1D Quantum Elasticity: superconductivity and Quantum Nematic Order
• Diagnosing Deconfinement and Topological Order
• Topology and Nematic Ordering I: A Gauge Theory
• Topological Defects on Fluctuating Surfaces: General Properties and the Kosterlitz-Thouless Transition
• Holographic Symmetries and Generalized Order Parameters for Topological Matter
• Experimental observables near a nematic quantum critical point in the pnictide and cuprate superconductors
• World Nematic Crystal Model of Gravity Explaining the Absence of Torsion
• Topological phases in two-dimensional arrays of parafermionic zero modes
• Properties and Detection of Spin Nematic Order in Strongly Correlated Electron Systems
• Quantum phase transition from an antiferromagnet to a spin liquid in a metal
• Fractionalized Phase in an XY-Z_2 Gauge Model
• Non-universal ordering of spin and charge in stripe phases
• Quantum hexatic order in two-dimensional dipolar and charged fluids
• Stripe melting and quantum criticality in correlated metals
• A Derivation of the Fradkin-Shenker Result From Duality: Links to Spin Systems in External Magnetic Fields and Percolation Crossovers
• Stripe fractionalization II: the quantum spin nematic and the Abrikosov lattice
• Critical behavior of 3D Z(N) lattice gauge theories at zero temperature
• Tendencies toward nematic order in YBa2Cu3O6+x: Uniform distortion vs. incipient charge stripes
• Deconfining the rotational Goldstone mode: the superconducting nematic liquid crystal in 2+1D
• The quantum smectic as a dislocation Higgs phase
• The Role of Quantum Fluctuations in the Hexatic Phase of Cold Polar Molecules
• Model of Fractionalization of Faraday Lines in Compact Electrodynamics

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