EPJ D Topical Review - The density matrix renormalization group for ab initio quantum chemistry

Over the past 15 years, the density matrix renormalisation group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS, viz. the rank of the decomposition, controls the size of the corner of the many-body Hilbert space that can be reached with the ansatz, and can be systematically increased until numerical convergence is reached. The MPS ansatz naturally captures exponentially decaying correlation functions, and the DMRG therefore works extremely well for noncritical one-dimensional systems.

Unfortunately, the active orbital spaces in quantum chemistry are often far from one-dimensional, and relatively large virtual dimensions are required to use the DMRG for ab initio quantum chemistry (QC-DMRG). In this EPJ D review article, the QC-DMRG algorithm, its computational cost, and its properties are discussed. Two important approaches that have been taken to reduce the computational cost are given special attention: orbital choice and ordering, and exploitation of the symmetry group of the Hamiltonian. The authors outline how, in combination with these approaches, the QC-DMRG algorithm allows the calculation of numerically exact solutions in active spaces of up to 40 electrons in 40 orbitals.

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Editors-in-Chief
Pere Roca i Cabarrocas and Daniel Lincot
ISSN: 2105-0716 (Electronic Edition)

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