Entanglement bipartitioning and tree tensor networks

TL;DR

This paper introduces an entanglement bipartitioning method to optimize tree tensor network structures for quantum many-body systems, leading to improved variational energies in spin models.

Contribution

It presents a novel entanglement bipartitioning approach to design more efficient TTNs tailored to specific quantum states.

Findings

Optimized TTNs outperform standard structures in variational energy calculations.

Entanglement bipartitioning reveals nontrivial tree structures for 1D and 2D Heisenberg models.

Method scales to systems of up to 16 sites, demonstrating practical applicability.

Abstract

We propose the entanglement bipartitioning approach to design an optimal network structure of the tree-tensor-network (TTN) for quantum many-body systems. Given an exact ground-state wavefunction, we perform sequential bipartitioning of spin-cluster nodes so as to minimize the mutual information or the maximum loss of the entanglement entropy associated with the branch to be bipartitioned. We demonstrate that entanglement bipartitioning of up to 16 sites gives rise to nontrivial tree network structures for $S=1/2$ Heisenberg models in one and two dimensions. The resulting TTNs enable us to obtain better variational energies, compared with standard TTNs such as uniform matrix product state and perfect-binary-tree tensor network.