Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States

Abstract

We develop the Density Matrix Renormalization Group (DMRG) technique for numerically studying incompressible fractional quantum Hall (FQH) states on the sphere. We calculate accurate estimates for ground state energies and excitationgaps at FQH filling fractions ν=1/3 and ν=5/2 for systems that are almost twice as large as the largest ever studied by exact diagonalization. We establish, by carefully comparing with existing numerical results on smaller systems, that DMRG is a highly effective numerical tool for studying incompressible FQH states.

5 pages, 4 figures

References in corpus (1)

• Entropy and Exact Matrix Product Representation of the Laughlin Wave Function

Cited by in corpus (6)

• Fractional Quantum Hall Hierarchy and the Second Landau Level
• The non-Abelian Interferometer
• Spin polarization of the $\nu =5/2$ quantum Hall state
• Density matrix renormalization group approach to two-fluid open many-fermion systems
• Multi-channel Kondo Models in non-Abelian Quantum Hall Droplets
• Topological Entropy of Quantum Hall States in Rotating Bose Gases