Neutral excitations of quantum Hall states: A density matrix renormalization group study

Abstract

We use the dynamical structure factors of the quantum Hall states at ν = 1/3 and ν = 1/2 in the lowest Landau level 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 are present and the finite-size effects can be understood using the fractional charge of the quasi-particle. At ν = 1/2, we find low energy modes with linear dispersion and the static structure factor ¯s(q) ∼ (q`)3 in the limit q` → 0. The properties of these modes agree quantitatively with the predictions of the composite-fermion theory placed on the infinite cylinder.