Polarized Fractional Quantum Hall States at 1/3 and 5/2 Filling: a Density-Matrix Renormalization Group Calculation

In this talk, the density-matrix renormalization group method is employed to investigate the fractional quantum Hall effect (FQHE) at filling numbers $\nu=1/3$ and $5/2$. We present benchmark results for both filling numbers for larger system sizes to show the accuracy as well as the capacity of our numerical algorithm. Furthermore, we demonstrate that by keeping a large number of states, one can also obtain reliable entanglement spectrum at $\nu=5/2$, which characterizes the topological properties of FQHE states. Based on a finite-size scaling analysis, we also confirm that the entanglement gap defined by Li and Haldane for $\nu=5/2$ state with Coulomb interaction remains finite in the thermodynamic limit.