Entanglement at the interplay between single- and many-bodyness

TL;DR

This paper analytically studies the entanglement properties of the Bethe chain's ground state using tensor networks, revealing the complex interplay between single- and many-body characteristics and challenging existing assumptions about tensor network constructions.

Contribution

It provides an analytical tensor network representation of the Bethe chain's ground state and highlights the necessity of longer-range unitaries for certain interacting systems.

Findings

Block entanglement peaks at the single- and many-body interplay

Ground states of interacting fermions require four-next-neighbor unitaries

Challenges the idea that ground states are obtainable via only next-neighbor operations

Abstract

The tensor network representation of the ground state of a Bethe chain is analytically obtained and studied in relation to its entanglement distribution. Block entanglement displays a maximum at the interplay between single- and many-bodyness. In systems of two fermions, tensor networks describing ground states of interacting Hamiltonians cannot be written as a sequence of next-neighbor unitaries applied on an uncorrelated state, but need four-next-neighbor unitaries in addition. This differs from the idea that the ground state can be obtained as a sequence of next-neighbor operations applied on a tensor network. The work uncovers the transcendence of the notion of many-bodyness in the implementation of protocols based on matrix product states.