title: Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms.
abstract: Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.
authors.affiliation: Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Garnet Kin-Lic
authors.initials: GK
authors.lastname: Chan
authors.affiliation: Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
authors.forename: Anna
authors.initials: A
authors.lastname: Keselman
authors.affiliation: Institute for Catalysis, Hokkaido University, Kita 21 Nishi 10, Sapporo, Hokkaido 001-0021, Japan.
authors.forename: Naoki
authors.initials: N
authors.lastname: Nakatani
authors.affiliation: Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Zhendong
authors.initials: Z
authors.lastname: Li
authors.affiliation: Department of Physics and Astronomy, University of California, Irvine, California 92697-4575, USA.
authors.forename: Steven R
authors.initials: SR
authors.lastname: White