Generic Construction of Efficient Matrix Product Operators

TL;DR

This paper introduces three novel compression methods for Matrix Product Operators, enabling efficient representations of complex operators in quantum many-body physics and quantum chemistry.

Contribution

It presents new compression techniques (Rescaled SVD, Deparallelisation, Delinearisation) for MPOs and demonstrates their effectiveness on various complex operators.

Findings

Efficient MPO representations of powers of spin-chain Hamiltonians

Construction of MPOs for complex 2D system Hamiltonians

Representation of long-range four-body Hamiltonians in quantum chemistry

Abstract

Matrix Product Operators (MPOs) are at the heart of the second-generation Density Matrix Renormalisation Group (DMRG) algorithm formulated in Matrix Product State language. We first summarise the widely known facts on MPO arithmetic and representations of single-site operators. Second, we introduce three compression methods (Rescaled SVD, Deparallelisation and Delinearisation) for MPOs and show that it is possible to construct efficient representations of arbitrary operators using MPO arithmetic and compression. As examples, we construct powers 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.