Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry

Abstract

Multilayer fractional quantum Hall wave functions can be used to construct the non-Abelian states of the ${\mathbb{Z}}_k$ Read-Rezayi series upon symmetrization over the layer index. Unfortunately, this construction does not yield the complete set of ${\mathbb{Z}}_k$ ground states on the torus. We develop an alternative projective construction of ${\mathbb{Z}}_k$ Read-Rezayi states that complements the existing one. On the multi-layer torus geometry, our construction consists of introducing twisted boundary conditions connecting the layers before performing the symmetrization. We give a comprehensive account of this construction for bosonic states, and numerically show that the full ground state and quasihole manifolds are recovered for all computationally accessible system sizes. Furthermore, we analyze the neutral excitation modes above the Moore-Read on the torus through an extensive exact diagonalization study. We show numerically that our construction can be used to obtain excellent approximations to these modes. Finally, we extend the new symmetrization scheme to the plane and sphere geometries.

19 pages, 9 figures

References in corpus (21)

• Non-Abelian Anyons and Topological Quantum Computation
• Fractional Quantum Hall States and Jack Polynomials
• Genons, twist defects, and projective non-Abelian braiding statistics
• Fractional topological insulators in three dimensions
• Quantum Hall system in Tao-Thouless limit
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $\alpha$
• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Degeneracy of non-abelian quantum Hall states on the torus: domain walls and conformal field theory
• Microscopic theory of the quantum Hall hierarchy
• Neutral Fermion Excitations in the Moore-Read state at ν=5/2
• Abelian and Non-Abelian States in $\nu =2/3$ Bilayer Fractional Quantum Hall Systems
• The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus
• Competing Abelian and non-Abelian topological orders in $\nu =1/3+1/3$ quantum Hall bilayers
• Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells
• Numerical Calculation of the Neutral Fermion Gap at $\nu =5/2$
• Bridge between Abelian and Non-Abelian Fractional Quantum Hall States
• From Irrational to Non-Unitary: on the Haffnian and Haldane-Rezayi wave functions
• Non-Abelian phases in two-component $\nu =2/3$ fractional quantum Hall states: Emergence of Fibonacci anyons
• Solvable models for unitary and non-unitary topological phases
• Possible non-Abelian Moore-Read state in double-layer bosonic fractional quantum Hall system

Cited by in corpus (19)

• Quantum Hall Physics - hierarchies and CFT techniques
• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Competing states for the fractional quantum Hall effect in the 1/3-filled second Landau level
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $\nu =1/2+1/2$ Bilayers
• Meron deconfinement in the quantum Hall bilayer at intermediate distances
• Constructing topological models by symmetrization: A PEPS study
• The Neutral Excitations in the Gaffnian State
• Signatures of Supersymmetry in the $\nu =5/2$ Fractional Quantum Hall Effect
• Phase diagram of $\nu =\frac{1}{2}+\frac{1}{2}$ bilayer bosons with inter-layer couplings
• Deformed Fredkin model for the $\nu =5/2$ Moore-Read state on thin cylinders
• Self-similarity of spectral response functions for fractional quantum Hall states
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Excitation and tunneling spectra of a fractional quantum Hall system in the thin cylinder limit
• Disorder-driven phase transitions in bosonic fractional quantum Hall liquids