Halperin (m, m',n) bilayer quantum Hall states on thin cylinders

Abstract

The Halperin $(m,m^{\prime },n)$ bilayer quantum Hall states are studied on thin cylinders. In this limit, charge density wave patterns emerge that are characteristic of the underlying quantum Hall state. The general patterns are worked out from a variant of the plasma analogy. Torus degeneracies are recovered, and for some important special cases a connection to well-known spin chain physics is made. By including interlayer tunneling, we also work out the critical behavior of a possible phase transition between the $(331)$ state and the non-abelian Moore-Read state in the thin cylinder limit.

published version

References in corpus (12)

• Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian statistics
• Incompressible Quantum Liquids and New Conservation Laws
• Laughlin State on Stretched and Squeezed Cylinders and Edge Excitations in Quantum Hall Effect
• Abelian and Non-abelian Hall Liquids and Charge Density Wave: Quantum Number Fractionalization in One and Two Dimensions
• The Ground State Structure and Modular Transformations of Fractional Quantum Hall States on a Torus
• The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus
• One-Dimensional Theory of the Quantum Hall System
• The Broken Symmetry of Two-Component $\nu =1/2$ Quantum Hall States
• Wavefunctions and counting formulas for quasiholes of clustered quantum Hall states on a sphere
• Domain wall type defects as anyons in phase space
• Parafermion statistics and the application to non-abelian quantum Hall states
• Hall Drag in Correlated Double Layer Quantum Hall Systems

Cited by in corpus (39)

• A theory of 2+1D bosonic topological orders
• A theory of 2+1D fermionic topological orders and fermionic/bosonic topological orders with symmetries
• Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory
• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros
• Competing states for the fractional quantum Hall effect in the 1/3-filled second Landau level
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Modular Matrices as Topological Order Parameter by Gauge Symmetry Preserved Tensor Renormalization Approach
• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• Fractional Quantum Hall Bilayers at Half-Filling: Tunneling-driven Non-Abelian Phase
• Repulsive Interactions in Quantum Hall Systems as a Pairing Problem
• Geometric construction of Quantum Hall clustering Hamiltonians
• S-duality constraints on 1D patterns associated with fractional quantum Hall states
• Gapless excitations in the Haldane-Rezayi state: The thin torus limit
• Pfaffian statistics through adiabatic transport in the 1D coherent state representation
• The structure of spinful quantum Hall states: a squeezing perspective
• Entangled Pauli Principles: the DNA of Quantum Hall Fluids
• Condensing non-Abelian quasiparticles
• Classification of Abelian and Non-Abelian Multilayer Fractional Quantum Hall States Through the Pattern of Zeros
• Zero modes, Bosonization and Topological Quantum Order: The Laughlin State in Second Quantization
• Solvable models for unitary and non-unitary topological phases
• Local two-body parent Hamiltonians for the entire Jain sequence
• Non-Abelian Two-component Fractional Quantum Hall States
• Abelian and non-Abelian statistics in the coherent state representation
• 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
• Topological order: from long-range entangled quantum matter to an unification of light and electrons
• Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing
• Modified Coulomb gas construction of quantum Hall states from non-unitary conformal field theories
• Composite fermions in Fock space: Operator algebra, recursion relations, and order parameters
• Gaffnian holonomy through the coherent state method
• Deformed Fredkin model for the $\nu =5/2$ Moore-Read state on thin cylinders
• Inner workings of fractional quantum Hall parent Hamiltonians: A matrix product state point of view
• Halperin $(m^{\prime },m,n)$ fractional quantum Hall effect in topological flat bands
• Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level
• Three-component fractional quantum Hall effect in topological flat bands
• Second-quantized approach to the study of Halperin state in fractional quantum Hall effect