We analyze the inner products of edge state wave functions 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 a recent work by J. Dubail, N. Read, and E. Rezayi [Phys. Rev. B 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.

• Received 30 January 2018

DOI:https://doi.org/10.1103/PhysRevB.97.155108