Naokazu Shibata 2003 J. Phys. A: Math. Gen. 36 R381 doi:10.1088/0305-4470/36/37/201
Naokazu Shibata
Show affiliationsThe 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.
Issue 37 (19 September 2003)
Received 27 March 2003, in final form 9 June 2003
Published 2 September 2003
Naokazu Shibata 2003 J. Phys. A: Math. Gen. 36 R381
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