Neutral Excitations of Quantum Hall States: a Density Matrix Renormalization Group Study

We use the dynamical structure factors of the quantum Hall states at ν=1/3 and ν=1/2 to study their excitation spectrum. Using the density matrix renormalization group in combination with the time-dependent variational principle on an infinite cylinder geometry, we extract the low energy properties. At ν=1/3, a sharp magnetoroton mode and the two-roton continuum agree with the fractionally charged quasi-particles picture. At ν=1/2, we find low energy modes with linear dispersion and the static structure factor s(q) ~ (q l_B)^3 in the limit q l_B → 0. The properties of these modes can be explained by the quasi-1D composite-fermion theory.