Fig. 1: Intrinsic metrics in FQH states.

The left panel shows that the fluctuations of the cyclotron metric \({\tilde{g}}_{ab}\) originate from the LL mixing. The right panel shows the hierarchical structure of the CHSs (denoted by dashed circles with different colors) of the corresponding model Hamiltonians (more details can be found in Table 2) in the lowest Landau level. Each of these spaces can have its own metric \({g}_{i}^{ab}\), the fluctuation around which can potentially lead to multiple GMs in a single Landau level.