Fractional quantum Hall states at 13 and 52 filling: Density-matrix renormalization group calculations

In this paper, the density-matrix renormalization group method is employed to investigate the fractional quantum Hall effect at filling fractions ν=1/3 and 5/2. We first present benchmark results at both filling fractions for large system sizes to show the accuracy as well as the capability of the numerical algorithm. Furthermore, we show that by keeping a large number of basis states, one can also obtain an accurate entanglement spectrum at ν=5/2 for large systems with electron numbers up to N_e=34, much larger than systems previously studied. Based on a finite-size scaling analysis, we demonstrate that the entanglement gap defined by Li and Haldane is finite in the thermodynamic limit, which characterizes the topological order of the fractional quantum Hall effect state.