Entanglement, fractional magnetization and long-range interactions

TL;DR

This paper proves that in quantum spin chains, significant fractional magnetization or long-range interactions necessarily lead to high entanglement, using the framework of Matrix Product States.

Contribution

It provides rigorous analytical proofs linking fractional magnetization, long-range interactions, and entanglement in quantum spin chains.

Findings

Large fractional magnetization implies high entanglement.

Long-range interactions are associated with increased entanglement.

Analytical proofs are established within the Matrix Product States framework.

Abstract

Based on the theory of Matrix Product States, we give precise statements and complete analytical proofs of the following claim: a large fractionalization in the magnetization or the need of long-range interactions imply large entanglement in the state of a quantum spin chain.