Resonant Raman scattering and numerical study in the fractional quantum Hall regime

We use a finite-size numerical method to address various issues related to resonant Raman scattering experiments in the fractional quantum Hall regime. We have calculated the excitation spectra and the multiple density correlation functions of such systems in the spherical geometry using the lowest Landau level approximation. We find that in the excitation spectra of a system at filling factor nu=1/3, at small wave-vectors, there are excited states at energies below that of the collective mode. The projected weights of these states into the two roton subspaces indicate that they are composite objects formed by two rotons with almost opposite momenta. We argue that these states could contribute significantly to Raman intensity in a resonant Raman scattering experiment. There are broad peaks in the projected dynamic structural factor near wave vectors ql(c) approximate to 2.2 and energies omega approximate to 0.2e(2)/epsilon l(c). These broad peaks remain, even when the filling factor moves away from the incompressible fillings. We conjecture that they are related to the short-range order of the system. We believe they are accessible in resonant Raman scattering on grated samples.