Energy-level statistics in strongly disordered systems with power-law hopping.

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 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 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 for small frequencies and for large frequencies , where is the characteristic matrix element of excitation hopping in a system of volume , and , and 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.