An efficient matrix product operator representation of the quantum chemical Hamiltonian

TLDR

Existing DMRG implementations for quantum chemistry rely on a traditional Hilbert‑space decimation formulation that outperforms straightforward matrix‑product‑based DMRG. The authors present an efficient method to construct the quantum‑chemical Hamiltonian as a matrix‑product operator. They implement this Hamiltonian within a DMRG algorithm that variationally optimizes matrix‑product states, representing operators as matrix‑product operators. The resulting MPO construction removes earlier performance drawbacks while retaining flexibility, allowing MPOs for abelian, non‑abelian, relativistic, and non‑relativistic models to be solved with the same program.

Abstract

We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from the point of view of Hilbert space decimation and attained higher performance compared to straightforward implementations of matrix product based DMRG. The latter variationally optimizes a class of ansatz states known as matrix product states, where operators are correspondingly represented as matrix product operators (MPOs). The MPO construction scheme presented here eliminates the previous performance disadvantages while retaining the additional flexibility provided by a matrix product approach, for example, the specification of expectation values becomes an input parameter. In this way, MPOs for different symmetries — abelian and non-abelian — and different relativistic and non-relativistic models may be solved by an otherwise unmodified program.