A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states

TL;DR

This paper introduces a flexible multi-reference perturbation theory method that minimizes the Hylleraas functional using matrix product states, providing accurate energies with scalable computational advantages.

Contribution

It presents a novel formulation of multi-reference perturbation theory that leverages matrix product states to achieve rigorous bounds and computational efficiency.

Findings

Accurate first order wavefunctions with sub-linear MPS bond dimension scaling.

No need to compute high-body density matrices.

Embarrassingly parallel algorithm scalable to many processors.

Abstract

We describe a formulation of multi-reference perturbation theory that obtains a rigorous upper bound to the second order energy by minimizing the Hylleraas functional in the space of matrix product states (MPS). The first order wavefunctions so obtained can also be used to compute the third order energy with little overhead. Our formulation has several advantages including (i) flexibility with respect to the choice of zeroth order Hamiltonian, (ii) recovery of the exact uncontracted multi-reference perturbation theory energies in the limit of large MPS bond dimension, (iii) no requirement to compute high body density matrices, (iv) an embarrassingly parallel algorithm (scaling up to the number of virtual orbitals, squared, processors). Preliminary numerical examples show that the MPS bond dimension required for accurate first order wavefunctions scales sub-linearly with the size of the basis.