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

Prashant Kumar, Frederick Duncan Michael Haldane

SciPost Phys. 16, 117 (2024) · published 1 May 2024

- doi: 10.21468/SciPostPhys.16.5.117
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### Abstract

We numerically compute the guiding center static structure factor $\bar S(k)$ of various fractional quantum Hall (FQH) states to $\mathcal{O}(k\ell)^6$ 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 $O(k\ell)^6$ 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.

### Cited by 1

### Authors / Affiliation: mappings to Contributors and Organizations

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^{1}Prashant Kumar, -
^{1}Frederick Duncan Michael Haldane

^{1}Princeton University