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

• Published in: Physics letters. A 2012-06, Vol.376 (30-31), p.2157-2161
• Main Authors: Hu, Zi-Xiang, Papić, Z., Johri, S., Bhatt, R.N., Schmitteckert, Peter
• Format: Article
• Language: English
• Subjects: Benchmarks; Convergence; Coulomb friction; Cylinders; Ground state; Halls; Quantum Hall effect; Solid state physics
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2012.05.031

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 ν=1/3 and ν=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. ► FQHE is a two-dimensional physics. ► Density-matrix renormalization group method applied to FQH systems. ► Benchmark study both on sphere and cylinder geometry.