TY - JOUR

T1 - Comparison of the density-matrix renormalization group method applied to fractional quantum Hall systems in different geometries

AU - Hu, Zi Xiang

AU - Papić, Z.

AU - Johri, S.

AU - Bhatt, R. N.

AU - Schmitteckert, Peter

N1 - Funding Information:
We would like to thank E.H. Rezayi, F.D.M. Haldane for simulating discussions. Z.-X. Hu also thanks Jize Zhao for comparing the results on the sphere. This work is supported by DOE grant No. DE-SC0002140 .

PY - 2012/6/18

Y1 - 2012/6/18

N2 - 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.

AB - 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.

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U2 - 10.1016/j.physleta.2012.05.031

DO - 10.1016/j.physleta.2012.05.031

M3 - Article

AN - SCOPUS:84861593724

SN - 0375-9601

VL - 376

SP - 2157

EP - 2161

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 30-31

ER -