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arXiv · 2304.14991

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

Prashant Kumar·F. D. M. Haldane
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Abstract

We numerically compute the guiding center static structure factor $\bar S(\bf k)$ 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.

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Prashant Kumar, F. D. M. Haldane. 2023-04-28. A numerical study of bounds in the correlations of fractional quantum Hall states. https://doi.org/10.21468/scipostphys.16.5.117

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