Automatic structural optimization of tree tensor networks

TL;DR

This paper introduces an algorithm for automatically optimizing the structure of tree tensor networks to better capture entanglement in quantum many-body systems, demonstrated on an antiferromagnetic Heisenberg spin chain.

Contribution

It presents a novel TTN optimization method that adjusts network structure via local reconnections to reduce entanglement, enhancing simulation accuracy.

Findings

Optimized TTN visualizes entanglement as a perfect binary tree.

Algorithm improves approximation of ground states.

Applicable to inhomogeneous quantum systems.

Abstract

Tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in improving its approximation accuracy. In this paper, we propose a TTN algorithm that enables us to automatically optimize the network structure by local reconnections of isometries to suppress the bipartite entanglement entropy on their legs. The algorithm can be seamlessly implemented to such a conventional TTN approach as density-matrix renormalization group. We apply the algorithm to the inhomogeneous antiferromagnetic Heisenberg spin chain having a hierarchical spatial distribution of the interactions. We then demonstrate that the entanglement structure embedded in the ground-state of the system can be efficiently visualized as a perfect binary tree in the optimized TTN. Possible improvements and applications of the algorithm are also discussed.