Table 1 Definition of various symbols used in the text

From: Geometric fluctuation of conformal Hilbert spaces and multiple graviton modes in fractional quantum Hall effect

\({\hat{R}}_{i}^{a}\)

Guiding center operator

\({\hat{\rho }}_{{{{{{{{\bf{q}}}}}}}}}\)

Guiding center density operator

\(\delta {\bar{\rho }}_{{{{{{{{\bf{q}}}}}}}}}\)

Regularized guiding center density operator

\({\hat{\pi }}_{ia}\)

Dynamical momentum operator

\({\bar{g}}^{ab}\)

Guiding center metric

\({\tilde{g}}^{ab}\)

Cyclotron metric

\({g}_{\alpha }^{ab}\)

Guiding center metric of CHS \({{{{{{{{\mathcal{H}}}}}}}}}_{\alpha }\)

Sq

Regularized guiding center structure factor

\({\hat{V}}_{\alpha }^{k{{{{{{{\rm{bdy}}}}}}}}}\)

k-body pseudopotential

\({\hat{{{{{{{{\mathcal{V}}}}}}}}}}_{\alpha }^{k{{{{{{{\rm{bdy}}}}}}}}}\)

Model Hamiltonian defined by \(\mathop{\sum }\nolimits_{i=1}^{\alpha }{\lambda }_{i}{\hat{V}}_{i}^{k{{{{{{{\rm{bdy}}}}}}}}}\)

\({{{{{{{{\mathcal{H}}}}}}}}}_{\alpha }^{k{{{{{{{\rm{bdy}}}}}}}}}\)

CHS determined by \({\hat{{{{{{{{\mathcal{V}}}}}}}}}}_{\alpha }^{k{{{{{{{\rm{bdy}}}}}}}}}\)

  1. Note that due to fermionic statistics, the constant coefficients λi in \({\hat{{{{{{{{\mathcal{V}}}}}}}}}}_{\alpha }^{k{{{{{{{\rm{bdy}}}}}}}}}\) might vanish. For example, \({\hat{{{{{{{{\mathcal{V}}}}}}}}}}_{3}^{2{{{{{{{\rm{bdy}}}}}}}}}={\lambda }_{1}{\hat{V}}_{1}^{k{{{{{{{\rm{bdy}}}}}}}}}+{\lambda }_{3}{\hat{V}}_{3}^{k{{{{{{{\rm{bdy}}}}}}}}}\) with λ2 = 0.