Entanglement bipartitioning and tree tensor networks

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.

9 pages, 8 figures

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Cited by in corpus (8)

• A tensor network view of multilayer multiconfiguration time-dependent Hartree methods
• Optimal Symbolic Construction of Matrix Product Operators and Tree Tensor Network Operators
• Statistical Mechanics Approach to the Holographic Renormalization Group: Bethe Lattice Ising Model and p-adic AdS/CFT
• State Diagrams to determine Tree Tensor Network Operators
• Variational quantum eigensolver with embedded entanglement using a tensor-network ansatz
• Automatic Structural Search of Tensor Network States including Entanglement Renormalization
• Improving accuracy of tree-tensor network approach by optimization of network structure
• TTNOpt: Tree tensor network package for high-rank tensor compression