S3 Quantum Hall Wavefunctions

Abstract

We construct a family of quantum Hall Hamiltonians whose ground states, at least for small system sizes, give correlators of the S3 conformal field theories. The ground states are considered as trial wavefunctions for quantum Hall effect of bosons at filling fraction nu=3/4 interacting either via delta function interaction or delta function plus dipole interaction. While the S3 theories can be either unitary or nonunitary, we find high overlaps with exact diagonalizations only for the nonunitary case, suggesting that these wavefunctions may correspond to critical points, possibly analogous to the previously studied Gaffnian wavefunction. These wavefunctions give an explicit example which cannot be fully characterized by their thin-torus limit or by their pattern of zeros.

4+epsilon pages. 1 figure. Revised version includes: 1 additional author; additional numerical work; several minor corrections. Our main results are unchanged

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• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Correlation Lengths and Topological Entanglement Entropies of Unitary and Non-Unitary Fractional Quantum Hall Wavefunctions
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Geometric construction of Quantum Hall clustering Hamiltonians
• Gapless excitations in the Haldane-Rezayi state: The thin torus limit
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Entanglement subspaces, trial wavefunctions, and special Hamiltonians in the fractional quantum Hall effect
• Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry
• Electron-Quasihole Duality and Second Order Differential Equation for Read-Rezayi and Jacks Wavefunctions
• Effective Edge State Dynamics in the Fractional Quantum Hall Effect
• Multi-Particle Pseudopotentials for Multi-Component Quantum Hall Systems
• Gaplessness of the Gaffnian
• The composite fermion theory revisited: a microscopic derivation without Landau level projection
• Construction of a series of new $\nu =2/5$ fractional quantum Hall wave functions by conformal field theory
• Spin-singlet Gaffnian wave function for fractional quantum Hall systems
• Conformal field theory construction for nonabelian hierarchy wave functions