DMRGbasierte

DMRGbasierte methods refer to computational approaches that implement the density matrix renormalization group (DMRG) to study quantum many-body systems. Originating in the 1990s, DMRG is a variational method particularly effective for one-dimensional strongly correlated lattices.

The central idea is to express the many-body wavefunction as a matrix product state (MPS) and to optimize the tensors by sweeping along the chain, keeping only the most relevant states via reduced density matrix truncation. The computational cost and accuracy are controlled by the bond dimension chi; larger chi captures more entanglement at higher cost.

DMRG-based methods have many extensions: time-dependent DMRG (tDMRG) for real- and imaginary-time evolution; finite-temperature formulations using purification or ancilla methods; and DMRG in quantum chemistry (DMRG-SCF) and other hybrids (DMET+DMRG). The German term DMRGbasierte is used in German-language literature to denote methods based on DMRG, and in English texts these are called DMRG-based methods.

Applications include 1D spin chains, Hubbard-type models, and other strongly correlated electrons, as well as quantum chemistry problems with large active spaces where traditional methods struggle.

Limitations: while highly effective in 1D and quasi-1D, performance degrades for highly entangled 2D systems; extending to higher dimensions typically requires tensor networks beyond MPS, such as PEPS, with greater computational demands. Ongoing research seeks more efficient algorithms, better environments for strong correlations, and integration with other quantum chemistry or embedding methods.

In practice, several software packages implement DMRG-based algorithms, including ITensor, TeNPy, Block, and ALPS, reflecting its continued role in computational physics and chemistry.