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 $\hat{I}½=1/3$ and $\hat{I}½=1/2$ 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 $\hat{I}½=1/3$, 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 $\hat{I}½=1/2$, we find low energy modes with linear dispersion and the static structure factor $\bar{s}(q)\sim (q\ell {)}^3$ in the limit $q\ell \to 0$. The properties of these modes agree quantitatively with the predictions of the composite-fermion theory placed on the infinite cylinder.

16 pages, 11 figures. Added subfigure 7c and some minor revisions