Inter-Landau-Level Pair Tunneling Rigidifies the Long-Wavelength Structure Factor of the ν=1/3 Laughlin State

Abstract

A textbook chain of reasoning, originating with Girvin, MacDonald, and Platzman, predicts that Landau-level mixing (LLM) at nu=1/3 should soften the long-wavelength structure factor S(L): virtual excitations suppress V_1, the magnetoroton gap closes, and the single-mode approximation then forces S(L) to increase. We test this chain on the Haldane sphere at nu=1/3, N=6, 2Q=15. (i) Perturbatively, via first-order Schrieffer-Wolff dressing of the LLL Laughlin state, fed Lowdin-renormalised pseudopotentials: the dressed state gives Delta S(1) at kappa=10 of approximately +21%, consistent with the GMP prediction (~19% softening of V_1^eff). (ii) Non-perturbatively, via rigorous two-Landau-level (LLL+SLL) exact diagonalisation using a repaired DiagHam 2LL module that retains, for the first time on the sphere, the full inter-LL scattering channels. The response reverses sign: S(1) rigidifies monotonically from 0.118 at kappa->0 to 0.080 at kappa=10, a 32% suppression. Perturbative and non-perturbative results thus disagree in sign, with a gap of ~53 percentage points between +21% (SW) and -32% (full ED). Channel-mask ablation localises the reversal to the DD<->UU pair-tunneling channel (98% of the shift). A four-way decomposition shows the three-body coherent content overpowers the perturbative admixture by ~2.5x. Repaired code: https://github.com/Cannan-1/DiagHamOnSphereOpenSource (v2.0).

This paper has been withdrawn by the authors due to the obsolescence of certain datasets and flaws identified in the original claims. We are completely reconstructing the arguments based on new evidence