2012/02/21 by Zi-Xiang Hu, Z. Papic, Zlatko Papić +4 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Boundary value problem #Convergence (economics) #Coulomb #Density matrix #Density matrix renormalization group #Electron #Fractional quantum Hall effect #Ground state #Hamiltonian (control theory) #Magnetic field #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Hall effect #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum electrodynamics #Quantum mechanics #Quantum spin Hall effect #Renormalization group #cond-mat.mes-hall #cond-mat.quant-gas #cond-mat.str-el
paper · pdf · doi:10.1016/j.physleta.2012.05.031
published as Phys. Lett. A 376, 2157(2012) · 5 pages, 7 figures
arxiv created 2012/02/21 · openalex publication_date 2012/05/16 · arxiv updated 2015/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.