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arXiv:2011.01247 · Physical Review Letters

Entanglement of Formation of Mixed Many-Body Quantum States via Tree Tensor Operators

L. Arceci, Pietro Silvi, S. Montangero

Published Jan 24, 2022• 14 citations
arXivHTMLPDF

Abstract

We present a numerical strategy to efficiently estimate bipartite entanglement measures, and in particular the entanglement of formation, for many-body quantum systems on a lattice. Our approach exploits the tree tensor operator tensor network Ansatz, a positive loopless representation for density matrices which, as we demonstrate, efficiently encodes information on bipartite entanglement, enabling the upscaling of entanglement estimation. Employing this technique, we observe a finite-size scaling law for the entanglement of formation in 1D critical lattice models at finite temperature for up to 128 spins, extending to mixed states the scaling law for the entanglement entropy.

DOI
10.1103/physrevlett.128.040501

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This work explores the use of a tree tensor network ansatz to simulate the ground state of a local Hamiltonian on a two-dimensional lattice. By exploiting the entropic area law, the tree tensor network ansatz seems to produce quasi-exact results in systems with sizes well beyond the reach of exact diagonalization techniques. We describe an optimization algorithm to accurately approximate ground states and apply it to the quantum Ising model on a torus of L X L sites for L= {4,6,8}. Approximate results for larger lattices are also obtained. As an application of the approach, we analyse the scaling of the ground state entropy at the quantum critical point of the model and confirm the presence of a logarithmic additive correction to the entropic area law.
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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 the uniform matrix product state and perfect binary tree tensor network.