Entanglement of formation of mixed many-body quantum states via Tree Tensor Operators

TL;DR

This paper introduces a numerical method using Tree Tensor Operator tensor networks to efficiently estimate bipartite entanglement, specifically the Entanglement of Formation, in many-body quantum systems, enabling analysis of larger systems and mixed states.

Contribution

The paper presents a novel tensor network approach for estimating entanglement of formation in mixed many-body quantum states, extending entanglement scaling laws to finite-temperature systems.

Findings

Finite-size scaling law for entanglement of formation in 1D critical models

Efficient encoding of bipartite entanglement in mixed states

Scalability to systems with up to 128 spins

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 up-scaling 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.