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

Quantum Hall Systems Studied by the Density Matrix Renormalization Group Method