Fractional quantum Hall states at 1/3 and 5/2 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 nu = 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 nu = 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 [Phys. Rev. Lett. 101, 010504 (2008)] is finite in the thermodynamic limit, which characterizes the topological order of the fractional quantum Hall effect state.