Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States

TL;DR

This paper introduces an adapted DMRG method to study large-scale incompressible fractional quantum Hall states on the sphere, providing accurate energies and gaps for larger systems than previously possible.

Contribution

The authors develop and validate a DMRG approach tailored for FQH states, enabling analysis of larger systems with improved accuracy over existing methods.

Findings

DMRG accurately estimates ground state energies and gaps for FQH states.

The method handles systems nearly twice as large as previous exact diagonalization studies.

DMRG proves to be an effective tool for studying incompressible FQH 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 \nu=1/3 and \nu=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.