  Motivated by neutral excitations in disordered electronic materials and
systems of trapped ultracold particles with long-range interactions, we study
energy-level statistics of quasiparticles with the power-law hopping
Hamiltonian $\propto 1/r^\alpha$ in a strong random potential. In solid-state
systems such quasiparticles, which are exemplified by neutral dipolar
excitations, lead to long-range correlations of local observables and may
dominate energy transport. Focussing on the excitations in disordered
electronic systems, we compute the energy-level correlation function
$R_2(\omega)$ in a finite system in the limit of sufficiently strong disorder.
At small energy differences the correlations exhibit Wigner-Dyson statistics.
In particular, in the limit of very strong disorder the energy-level
correlation function is given by $R_2(\omega,V)=A_3\frac{\omega}{\omega_V}$ for
small frequencies $\omega\ll\omega_V$ and
$R_2(\omega,V)=1-(\alpha-d)A_{1}\left(\frac{\omega_V}{\omega}\right)^\frac{d}{\alpha}
-A_2\left(\frac{\omega_V}{\omega}\right)^2$ for large frequencies
$\omega\gg\omega_V$, where $\omega_V\propto V^{-\frac{\alpha}{d}}$ is the
characteristic matrix element of excitation hopping in a system of volume $V$,
and $A_1$, $A_2$ and $A_3$ are coefficient of order unity which depend on the
shape of the system. The energy-level correlation function, which we study,
allows for a direct experimental observation, for example, by measuring the
correlations of the ac conductance of the system at different frequencies.
