Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in fractional quantum Hall effect

A fundamental manifestation of the nontrivial correlations of an incompressible fractional quantum Hall (FQH) state is that an electron added to it disintegrates into more elementary particles, namely fractionally-charged composite fermions (CFs). We show here that the Girvin-MacDonald-Platzman (GMP) density-wave excitation of the $\nu{=}n/(2pn{\pm }1)$ FQH states also splits into more elementary single CF excitons. In particular, the GMP graviton, which refers to the recently observed spin-2 neutral excitation in the vanishing wave vector limit [Liang {\it et al.}, Nature {\bf 628}, 78 (2024)], remains undivided for $\nu{=}n/(2n{\pm} 1)$ but splits into two gravitons at $\nu{=}n/(4n{\pm} 1)$ with $n{>}1$. A detailed experimental confirmation of the many observable consequences of the splitting of the GMP mode should provide a unique window into the correlations underlying the FQH effect.