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to a description in terms of an excited rotating/vibrating quantal molecule. Specific examples of the reducibility of the JL and Moore-Read states to the molecular descrip- tion introduced in this paper are provided in Sections III C and III D. This is a surprising result, since these Jastrow based trial functions are widely described in the previous literature as being liquid-like in an essential way. 

For completeness and clarity in the presentation, we briefly provide in this section a graphical illustration of some of the main characteristics of the LLL spectra, cal- culated via the exact-diagonalization approach. 

First we describe here the special form [11, 15, 30] of the many-body Hamiltonian used for calculating the global ground state of a finite number N of electrons at 

## B. Characteristic properties of the lowest-Landau-level spectra 

a given magnetic field B . This special form takes advan- tage of the simplifications at the limit of large B , i.e., when the relevant Hilbert space can be restricted to the lowest Landau level, given that ¯ hω$_{0}$ << ¯ hω$_{c}$/ 2; the fre- quency ω$_{0}$ specifies the external harmonic confinement and ω$_{c}$ = eB/ ( mc ) is the cyclotron frequency. Then the many-body hamiltonian reduces to 

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where L = ∑ N i $_{=1}$l$_{i}$ is the total angular momentum and z = x + iy . In the case of N rapidly rotating bosons (with ω$_{0}$ spec- 

ifying the external confinement of the two-dimensional harmonic trap and Ω denoting the rotational frequency), the corresponding Hamiltonian [24, 25, 29, 45] (in the limit Ω /ω$_{0}$ → 1) is written as [46] 

Since we will consider many-body energy eigenstates that are eigenstates of the total angular momentum as well, it follows that only the interaction terms are non- trivial in both Hamiltonians (1) and (2). As a result, we will henceforth follow the practice of focussing on the simpler interaction-only LLL Hamiltonian 

where v ( z$_{i}$ − z$_{j}$ ) denotes the two-body interaction (Coulomb for electrons and repulsive contact potential for bosons). The “ground states” of the Hamiltonian in Eq. (3) coincide with the “yrast” band [36]. 

We remind the reader that the EXD method is based on the fact that the full LLL Hilbert space at a given total angular momentum L is spanned by the set of all possible uncorrelated permanents (for bosons) or Slater determinants (for electrons) made out from the Darwin- Fock zero-node single-particle levels (referred to also as orbitals) 

with l$_{i}$ ≥ 0. The position variable z is given in units of Λ = √ ¯ h/ ( mω$_{0}$ ) in the case of a rotating harmonic trap (with lateral confinement frequency ω$_{0}$ ) or $_{l$_{B}$}$√$_{2 in the}$ case of an applied magnetic field B , with l$_{B}$ = √ ¯ h/ ( mω$_{c}$ ) being the magnetic length and ω$_{c}$ the cyclotron frequency [46]. (For details concerning the EXD method, see, e.g., Refs. [15, 29].) In the following, we use the convention 

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