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

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 sta...

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Bibliographic Details
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
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Summary: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.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2012.05.031