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Structure of edge-state inner products in the fractional quantum Hall effect

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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… Click to show full abstract

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.

Keywords: edge state; inner; quantum hall; fractional quantum; hall effect; inner products

Journal Title: Physical Review B
Year Published: 2018

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