Link representation of the entanglement entropies for all bipartitions

TL;DR

This paper introduces approximation techniques for representing entanglement entropies as link strengths in quantum states, enabling insights into their geometric entanglement structure, with applications to specific many-body systems.

Contribution

It proposes new methods to approximate entanglement links in various quantum states, improving understanding of their geometric entanglement structure.

Findings

Approximation techniques achieve high accuracy for matrix product and free fermionic states.

Link representation reveals geometric features of entanglement in complex quantum systems.

Applications to spin chains demonstrate the method's physical relevance.

Abstract

We have recently shown that the entanglement entropy of any bipartition of a quantum state can be approximated as the sum of certain link strengths connecting internal and external sites. The representation is useful to unveil the geometry associated with the entanglement structure of a quantum many-body state which may occasionally differ from the one suggested by the Hamiltonian of the system. Yet, the obtention of these entanglement links is a complex mathematical problem. In this work, we address this issue and propose several approximation techniques for matrix product states, free fermionic states, or in cases in which contiguous blocks are specially relevant. Along with this, we discuss the accuracy of the approximation for different types of states and partitions. Finally, we employ the link representation to discuss two different physical systems: the spin-1/2 long-range XXZ chain and the spin-1 bilinear biquadratic chain.