Density-matrix renormalization using three classes of block states

An extension of the density-matrix renormalization-group (DMRG) method is p resented. Besides the two groups or classes of block states considered in W hite's formulation, the retained nz states, and the neglected ones, we intr oduce an intermediate group of block states having the following p largest eigenvalues hi of the reduced density matrix: lambda(1)greater than or equa l to...greater than or equal to lambda(m)greater than or equal to lambda(m1)greater than or equal to...greater than or equal to lambda(m+p). These st ates are taken into account when they contribute to intrablock transitions but are neglected when they participate in more delocalized interblock fluc tuations. Applications to one-dimensional models (Heisenberg, Hubbard, and dimerized tight binding) show that in this way the involved computer resour ces can be reduced without significant loss of accuracy. The efficiency and accuracy of the method is analyzed by varying m and p and by comparison wi th standard DMRG calculations. A Hamiltonian-independent scheme for choosin g m and p and for extrapolating to the limit where m and p are infinite is provided. Finally, an extension of the 3-classes approach is outlined, whic h incorporates the fluctuations between the p states of different blocks as a self-consistent dressing of the block interactions among the retained m states. [S0163-1829(98)03943-5].