Matrix Product Operators, Matrix Product States, and ab initio Density Matrix Renormalization Group algorithms

摘要

Current descriptions of the ab initio DMRG algorithm use two superficiallydifferent languages: an older language of the renormalization group andrenormalized operators, and a more recent language of matrix product states andmatrix product operators. The same algorithm can appear dramatically differentwhen written in the two different vocabularies. In this work, we carefullydescribe the translation between the two languages in several contexts. First,we describe how to efficiently implement the ab-initio DMRG sweep using amatrix product operator based code, and the equivalence to the originalrenormalized operator implementation. Next we describe how to implement thegeneral matrix product operator/matrix product state algebra within a purerenormalized operator-based DMRG code. Finally, we discuss two improvements ofthe ab initio DMRG sweep algorithm motivated by matrix product operatorlanguage: Hamiltonian compression, and a sum over operators representation thatallows for perfect computational parallelism. The connections andcorrespondences described here serve to link the future developments with thepast, and are important in the efficient implementation of continuing advancesin ab initio DMRG and related algorithms.