Application of the density matrix renormalization group method to finite temperatures and two-dimensional systems

摘要

The density matrix renormalization group (DMRG) method and its applicationsto finite temperatures and two-dimensional systems are reviewed. The basic ideaof the original DMRG method, which allows precise study of the ground stateproperties and low-energy excitations, is presented for models which includelong-range interactions. The DMRG scheme is then applied to the diagonalizationof the quantum transfer matrix for one-dimensional systems, and a reliablealgorithm at finite temperatures is formulated. Dynamic correlation functionsat finite temperatures are calculated from the eigenvectors of the quantumtransfer matrix with analytical continuation to the real frequency axis. Anapplication of the DMRG method to two-dimensional quantum systems in a magneticfield is demonstrated and reliable results for quantum Hall systems arepresented.