Density-matrix renormalization using three classes of block states

TL;DR

This paper introduces an extension to the density matrix renormalization group method by adding an intermediate class of block states, improving computational efficiency while maintaining accuracy in one-dimensional quantum models.

Contribution

The authors propose a novel three-class block state scheme for DMRG, enhancing efficiency and accuracy over traditional two-class approaches.

Findings

Reduced computational resources without significant accuracy loss.

Effective scheme for choosing parameters m and p.

Comparable results to standard DMRG in model applications.

Abstract

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.