Quantum Hall Systems Studied by the Density Matrix Renormalization Group Method

TL;DR

This paper applies the DMRG method to study quantum Hall systems, revealing their phase diagram and various states, including liquids, CDW states, and transitions in bilayer systems.

Contribution

It introduces the use of DMRG for quantum Hall systems, providing detailed phase diagrams and insights into state transitions not previously explored with this method.

Findings

Identified various quantum Hall states including stripe, bubble, and Wigner crystal phases.

Analyzed spin transitions and domain formations at v=2/3.

Investigated state evolution in bilayer systems at v=1.

Abstract

The ground-state and low-energy excitations of quantum Hall systems are studied by the density matrix renormalization group (DMRG) method. From the ground-state pair correlation functions and low-energy excitions, the ground-state phase diagram is determined, which consists of incompressible liquid states, Fermi liquid type compressible liquid states, and many kinds of CDW states called stripe, bubble and Wigner crystal. The spin transition and the domain formation are studied at v=2/3. The evolution from composite fermion liquid state to an excitonic state in bilayer systems is investigated at total filling factor v=1.