Density-matrix renormalization using three classes of block states

Details Density-matrix renormalization using three classes of block states Density-matrix renormalization using three classes of block states

1998-09-17

arxiv.org/abs/cond-mat/9809233v1

Physics

Condensed Matter

Strongly Correlated Electrons

16 pages, 4 figures

Scientific paper

10.1103/PhysRevB.58.12691

An extension of the the density matrix renormalization group (DMRG) method is presented. Besides the two groups or classes of block states considered in White's formulation, the retained $m$ states and the neglected ones, we introduce an intermediate group of block states having the following $p$ largest eigenvalues $\lambda_i$ of the reduced density matrix: $\lambda_1 \ge >... \lambda_m \ge \lambda_{m+1}\ge ... \ge \lambda_{m+p}$. These states are taken into account when they contribute to intrablock transitions but are neglected when they participate in more delocalized interblock fluctuations. Applications to one-dimensional models (Heisenberg, Hubbard and dimerized tight-binding) show that in this way the involved computer resources 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 with standard DMRG calculations. A Hamiltonian-independent scheme for choosing $m$ 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, which incorporates the fluctuations between the $p$ states of different blocks as a self-consistent dressing of the block interactions among the retained $m$ states.

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