Chapter 4 - Density matrix renormalization group for ab initio quantum chemistry Hamiltonian

Abstract

The implementation of density matrix renormalization group (DMRG) in ab initio quantum chemistry is usually much more complicated than that in condensed matter physics models, due to the lack of spatial translation symmetry and the presence of the four-body and long-range interaction terms. In this chapter we focus on the practical aspects of ab initio DMRG implementation. First, the traditional DMRG and matrix product states-based algorithms for ab initio Hamiltonians as well as the scheme of optimal construction for matrix product operators are introduced. Then, we discuss techniques for adopting symmetries and spin adaption, calculating n-electron reduced density matrix, selecting and ordering the active molecule orbitals, as well as analyzing DMRG wavefunction. Finally, most representative ab initio DMRG directions are briefly reviewed, including DMRG for larger active spaces, relativistic DMRG, and high-performance ab initio DMRG as well as tensor network states for ab initio quantum chemistry.