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

TL;DR

This paper systematically compares the application of the density-matrix renormalization group method to fractional quantum Hall systems in sphere and cylinder geometries, highlighting convergence behaviors and efficiency differences.

Contribution

It provides a detailed convergence analysis and benchmarks for DMRG applied to FQHE in different geometries, emphasizing the advantages of the cylinder geometry.

Findings

Rapid convergence observed in cylinder geometry

Ground state energies at ν=1/3 and ν=5/2 accurately extracted

Cylinder geometry is particularly suitable for DMRG in FQHE

Abstract

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.