The Density Matrix Renormalization Group for Strong Correlation in Ground and Excited States

Abstract

The density matrix renormalization group (DMRG), originally introduced by White in 1992 in solid state physics, has since found numerous applications in quantum chemistry. DMRG allows one to approximate the full CI wave function with polynomial scaling, making active spaces with about 100 orbitals accessible. Together with self-consistent field orbital optimization (DMRG-SCF), it allows for much larger active spaces than the complete active space self-consistent field (CASSCF) method. In this chapter, we provide an introduction to the theory behind DMRG, both in the original renormalization group formulation, as well as in the more modern formulation where wave functions and operators are represented as matrix product states and matrix product operators, respectively. We further discuss quantum-information-theoretical orbital entanglement measures that are accessible through DMRG, which pave the way to automated active space selection in multicongurational calculations, and factors that control DMRG convergence and accuracy. Finally, we review modern developments in and around DMRG, such as post-DMRG methods for the description of dynamic correlation and environment effects, tensor network states, as well as applications of DMRG and DMRG-SCF in quantum chemistry.