Density matrix renormalization group for bosonic quantum Hall effect

We developed a density matrix renormalization group technique to study quantum Hall fractions of fast rotating bosons. In this paper, we present a discussion of the method together with the results which we obtain in three distinct cases of the narrow-channel, cylinder, and spherical geometries. In the narrow-channel case, which is relevant to anisotropic confining traps in the limit of extremely fast rotation, we find a series of zero-temperature phase transitions in the strongly interacting regime as a function of the interaction strength between bosons. We compute energies and density profiles for different filling fractions on a cylinder and compare the convergence rates of the method in the cylinder and a sphere geometries.