Generic construction of efficient matrix product operators

摘要

Matrix product operators (MPOs) are at the heart of the second-generation density matrix renormalizationgroup (DMRG) algorithm formulated in matrix product state language. We first summarize the widely knownfacts on MPO arithmetic and representations of single-site operators. Second, we introduce three compressionmethods (rescaled SVD, deparallelization, and delinearization) forMPOs and show that it is possible to constructefficient representations of arbitrary operators usingMPO arithmetic and compression. As examples,we constructpowers of a short-ranged spin-chain Hamiltonian, a complicated Hamiltonian of a two-dimensional system and,as proof of principle, the long-range four-body Hamiltonian from quantum chemistry.