On the Structure of Edge State Inner Products in the Fractional Quantum Hall Effect

TL;DR

This paper investigates the inner products of edge state wavefunctions in fractional quantum Hall systems, confirming a high-order symmetry-constrained large-N expansion ansatz through exact numerical comparisons.

Contribution

It provides a detailed high-order analysis of the edge state inner products and validates the effective large-N expansion ansatz against exact calculations.

Findings

High-order symmetry constraints improve the ansatz accuracy.

Exact overlaps match the large-N expansion predictions.

The effective description is highly accurate for small system sizes.

Abstract

We analyse the inner products of edge state wavefunctions in the fractional quantum Hall effect, specifically for the Laughlin and Moore-Read states. We use an effective description for these inner products given by a large-$N$ expansion ansatz proposed in recent work by J. Dubail, N. Read and E. Rezayi, PRB 86, 245310 (2012). As noted by these authors, the terms in this ansatz can be constrained using symmetry, a procedure we perform to high orders. We then check this conjecture by calculating the overlaps exactly for small system sizes and compare the numerics with our high-order expansion. We find the effective description to be very accurate.