  The density matrix renormalization group (DMRG) method and its applications
to finite temperatures and two-dimensional systems are reviewed. The basic idea
of the original DMRG method, which allows precise study of the ground state
properties and low-energy excitations, is presented for models which include
long-range interactions. The DMRG scheme is then applied to the diagonalization
of the quantum transfer matrix for one-dimensional systems, and a reliable
algorithm at finite temperatures is formulated. Dynamic correlation functions
at finite temperatures are calculated from the eigenvectors of the quantum
transfer matrix with analytical continuation to the real frequency axis. An
application of the DMRG method to two-dimensional quantum systems in a magnetic
field is demonstrated and reliable results for quantum Hall systems are
presented.
