S3 Quantum Hall Wavefunctions

TL;DR

This paper constructs quantum Hall wavefunctions based on S3 conformal field theories, exploring their properties and overlaps with exact solutions, and suggesting they may represent critical points in quantum Hall systems.

Contribution

It introduces a new family of quantum Hall trial wavefunctions derived from S3 conformal field theories, including analysis of their overlaps and critical behavior.

Findings

High overlaps with exact solutions for nonunitary S3 theories

Wavefunctions may correspond to critical points in quantum Hall systems

Explicit examples not characterized by thin-torus limit or pattern of zeros

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.