Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm

TL;DR

This paper introduces an efficient algorithm for tree tensor network states in quantum chemistry, offering a more flexible entanglement representation than matrix product states, with demonstrated advantages in certain molecular systems.

Contribution

The paper presents an optimal tree tensor network state algorithm with half-renormalization, improving computational efficiency and extending the applicability of tensor networks in quantum chemistry.

Findings

Tree tensor network states require fewer renormalized states for similar accuracy.

Tree tensor networks outperform matrix product states in tree-like molecules.

Demonstrated correlation of 110 electrons in 110 orbitals using tree tensor networks.

Abstract

We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and \pi-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an ilustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.