Massive Higher-Spin Fields in the Fractional Quantum Hall Effect
arXiv:2404.16013 · doi:10.1103/PhysRevB.110.235152
Abstract
Incompressibility plays a key role in the geometric description of fractional quantum Hall fluids. It is naturally related to quantum area-preserving diffeomorphisms and the underlying Girvin-MacDonald-Plazman algebra, which gives rise to an emergent non-relativistic massive spin-2 mode propagating in the bulk. The corresponding metric tensor can be identified with a nematic order parameter for the bulk states. In the linearised regime with a flat background, it has been shown that this mode can be described by a spin-2 Schroedinger action. However, quantum area-preserving diffeomorphisms also suggest the existence of higher-spin modes that cannot be described through nematic fractional quantum Hall states. Here, we consider p-atic Hall phases, in which the corresponding p-atic order parameters are related to higher-rank symmetric tensors. We then show that in this framework, non-relativistic massive chiral higher-spin fields naturally emerge and that their dynamics is described by higher-spin Schroedinger actions. We finally show that these effective actions can be derived from relativistic massive higher-spin theories in 2+1 dimensions after taking a non-relativistic limit.
10 pages, published version
References in corpus (61)
- Topological Insulators
- Topological insulators and superconductors
- Zoo of quantum-topological phases of matter
- Nematic Fermi Fluids in Condensed Matter Physics
- Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
- Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
- Two-Dimensional Matter: Order, Curvature and Defects
- Geometrical Description of the Fractional Quantum Hall Effect
- Theory of Banana Liquid Crystal Phases and Phase Transitions
- Dual gauge field theory of quantum liquid crystals in two dimensions
- Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
- Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect
- Frame-like gauge invariant formulation for massive high spin particles
- Bimetric Theory of Fractional Quantum Hall States
- Field theory of the quantum Hall nematic transition
- Maxwell-like Lagrangians for higher spins
- Chiral Gravitons in Fractional Quantum Hall Liquids
- Theory of Nematic Fractional Quantum Hall State
- Geometric adiabatic transport in quantum Hall states
- Spectral Sum Rules and Magneto-Roton as Emergent Graviton in Fractional Quantum Hall Effect
- Higher-Spin Theory of the Magnetorotons
- FQHE on curved backgrounds, free fields and large N
- Theory of Quantum Hall Nematics
- Transverse Invariant Higher Spin Fields
- Bosons, fermions and anyons in the plane, and supersymmetry
- Investigating anisotropic quantum Hall states with bi-metric geometry
- Effective Field Theory of Fractional Quantized Hall Nematics
- Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect
- Geometric quench and nonequilibrium dynamics of fractional quantum Hall states
- Topologically Massive Higher Spin Gravity
- Non-relativistic fields from arbitrary contracting backgrounds
- Evidence of a fractional quantum Hall nematic phase in a microscopic model
- Consistent deformations of free massive field theories in the Stueckelberg formulation
- On massive gravitons in 2+1 dimensions
- Fractional quantum Hall systems near nematicity: bimetric theory, composite fermions, and Dirac brackets
- A spin-4 analog of 3D massive gravity
- Possible nematic to smectic phase transition in a two-dimensional electron gas at half-filling
- Octupolar order in two dimensions
- Multipole Expansion in the Quantum Hall Effect
- Hydrodynamic theory of atic liquid crystals
- High Spin Topologically Massive Gravity
- Classification of nematic order in 2+1D: Dislocation melting and lattice gauge theory
- Long-ranged order and flow alignment in sheared atic liquid crystals
- Microscopic Model for Fractional Quantum Hall Nematics
- Gravity and the spin-2 planar Schroedinger equation
- Collective excitations at filling factor 5/2: The view from superspace
- Geometric quench in the fractional quantum Hall effect: exact solution in quantum Hall matrix models and comparison with bimetric theory
- Higher-spin gauge theories in three spacetime dimensions
- Quantum Hall Liquid Crystals
- Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State
- Signatures of Supersymmetry in the Fractional Quantum Hall Effect
- On higher spin analogues of linearized Topologically Massive Gravity and linearized "New Massive Gravity"
- Extended Nappi-Witten Geometry for the Fractional Quantum Hall Effect
- Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
- Quantum Emulation of Gravitational Waves
- Induced topological order at the boundary of 3D topological superconductors
- Specific heat of 2D interacting Majorana fermions from holography
- Nested Defects on the Boundary of Topological Superconductors
- Noncommutative Geometry and Deformation Quantization in the Quantum Hall Fluids with Inhomogeneous Magnetic Fields
- Massless spin 2 interacting with massive higher spins in d=3
- Adiabatic Deformations of Quantum Hall Droplets