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

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

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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 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.

Original languageEnglish (US)
Pages (from-to)2157-2161
Number of pages5
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume376
Issue number30-31
DOIs
StatePublished - Jun 18 2012

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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