  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.
