APPROXIMATE DIAGONALIZATION USING THE DENSITY-MATRIX RENORMALIZATION-GROUP METHOD - A 2-DIMENSIONAL-SYSTEMS PERSPECTIVE

In order to extend the density-matrix renormalization-group (DMRG) met hod to two-dimensional systems, we formulate two alternative methods t o prepare the initial states. We find that the number of states that i s needed for accurate energy calculations grows exponentially with the linear system size. We also analyze how the states kept in the DMRG m ethod manage to preserve both the intrablock and interblock Hamiltonia ns, which is the key to the high accuracy of the method. We also prove that the energy calculated on a finite cluster is always a variationa l upper bound.