S-duality constraints on 1D patterns associated with fractional quantum Hall states

Abstract

Using the modular invariance of the torus, constraints on the 1D patterns are derived that are associated with various fractional quantum Hall ground states, e.g. through the thin torus limit. In the simplest case, these constraints enforce the well known odd-denominator rule, which is seen to be a necessary property of all 1D patterns associated to quantum Hall states with minimum torus degeneracy. However, the same constraints also have implications for the non-Abelian states possible within this framework. In simple cases, including the $\nu =1$ Moore-Read state and the $\nu =3/2$ level 3 Read-Rezayi state, the filling factor and the torus degeneracy uniquely specify the possible patterns, and thus all physical properties that are encoded in them. It is also shown that some states, such as the "strong p-wave pairing state", cannot in principle be described through patterns.

4+epsilon pages, 1 figure, RevTeX4

References in corpus (13)

• Fractional Quantum Hall States and Jack Polynomials
• Quantum Hall system in Tao-Thouless limit
• Half-Filled Lowest Landau Level on a Thin Torus
• Abelian and Non-abelian Hall Liquids and Charge Density Wave: Quantum Number Fractionalization in One and Two Dimensions
• The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus
• One-Dimensional Theory of the Quantum Hall System
• Degeneracy of non-abelian quantum Hall states on the torus: domain walls and conformal field theory
• A classification of symmetric polynomials of infinite variables -- a construction of Abelian and non-Abelian quantum Hall states
• Halperin (m, m',n) bilayer quantum Hall states on thin cylinders
• Pfaffian statistics through adiabatic transport in the 1D coherent state representation
• Domain wall type defects as anyons in phase space
• Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras
• Domain walls, fusion rules and conformal field theory in the quantum Hall regime

Cited by in corpus (25)

• Topological Flat Band Models and Fractional Chern Insulators
• Nonlinearity induced topological physics in momentum space and real space
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Repulsive Interactions in Quantum Hall Systems as a Pairing Problem
• Entanglement Scaling of Fractional Quantum Hall states through Geometric Deformations
• Gapless excitations in the Haldane-Rezayi state: The thin torus limit
• The structure of spinful quantum Hall states: a squeezing perspective
• Entangled Pauli Principles: the DNA of Quantum Hall Fluids
• Zero modes, Bosonization and Topological Quantum Order: The Laughlin State in Second Quantization
• Local two-body parent Hamiltonians for the entire Jain sequence
• The Jain-2/5 parent Hamiltonian: structure of zero modes, dominance patterns, and zero mode generators
• Algebraic approach to the study of zero modes of Haldane pseudopotentials
• Devil's staircase phase diagram of the fractional quantum Hall effect in the thin-torus limit
• Abelian and non-Abelian statistics in the coherent state representation
• Thin torus perturbative analysis of elementary excitations in the Gaffnian and Haldane-Rezayi quantum Hall states
• Topological order: from long-range entangled quantum matter to an unification of light and electrons
• Search for exact local Hamiltonians for general fractional quantum Hall states
• Effective spin chains for fractional quantum Hall states
• Gaplessness of the Gaffnian
• Composite fermions in Fock space: Operator algebra, recursion relations, and order parameters
• Beyond the Tao-Thouless limit of the fractional quantum Hall effect: spin chains and Fermi surface deformation
• Gaffnian holonomy through the coherent state method
• Heat equation approach to geometric changes of the torus Laughlin-state
• Inner workings of fractional quantum Hall parent Hamiltonians: A matrix product state point of view
• Jack on a Devil's staircase