1202.4697 (Zi-Xiang Hu et al.)

Comparison of the density-matrix renormalization group method applied to
fractional quantum Hall systems in different geometries    [PDF]

Zi-Xiang Hu, Z. Papic, S. Johri, R. N. Bhatt, Peter Schmitteckert

We report a systematic study of the fractional quantum Hall effect (FQHE)
using the density-matrix renormalization group (DMRG) method on two different
geometries: the sphere and the cylinder. We provide convergence benchmarks
based on model Hamiltonians known to possess exact zero-energy ground states,
as well as an analysis of the number of sweeps and basis elements that need to
be kept in order to achieve the desired accuracy.The ground state energies of
the Coulomb Hamiltonian at $\nu=1/3$ and $\nu=5/2$ filling are extracted and
compared with the results obtained by previous DMRG implementations in the
literature. A remarkably rapid convergence in the cylinder geometry is noted
and suggests that this boundary condition is particularly suited for the
application of the DMRG method to the FQHE.

View original: http://arxiv.org/abs/1202.4697