A numerical study of bounds in the correlations of fractional quantum Hall states

Abstract

We numerically compute the guiding center static structure factor $\bar{S}(\mathbf{k})$ of various fractional quantum Hall (FQH) states to $\mathcal{O}\left((k\ell {)}^6\right)$ where $k$ is the wavenumber and $\ell$ is the magnetic length. Employing density matrix renormalization group on an infinite cylinder of circumference $L_y$, we study the two-dimensional limit using $L_y/\xi \gg 1$, where $\xi$ is the correlation length. The main findings of our work are: 1) the ground states that deviate away from the ideal conformal block wavefunctions, do not saturate the Haldane bound, and 2) the coefficient of $O\left((k\ell {)}^6\right)$ term appears to be bounded above by a value predicted by field theories proposed in the literature. The first finding implies that the graviton mode is not maximally chiral for experimentally relevant FQH states.

14 pages, 2 figures, minor revisions

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Cited by in corpus (4)

• Theory of fractional quantum Hall liquids coupled to quantum light and emergent graviton-polaritons
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Corner Charge Fluctuations and Many-Body Quantum Geometry
• Chiral Graviton Modes in Fermionic Fractional Chern Insulators