Entanglement, Haag-duality and type properties of infinite quantum spin chains

TL;DR

This paper explores how the entanglement properties of infinite quantum spin chains relate to the algebraic type of their observable algebras, revealing deep connections between algebraic structure and entanglement.

Contribution

It establishes a link between the von Neumann algebra type of half-chain observables and the nature of entanglement in infinite quantum spin chains, including the critical XY model.

Findings

Only type I algebras support standard entanglement theory with density operators.

Non-type I algebras exhibit infinite entanglement, allowing distillation of infinite maximally entangled pairs.

The ground state of the critical XY model exemplifies this infinite entanglement property.

Abstract

We consider an infinite spin chain as a bipartite system consisting of the left and right half-chain and analyze entanglement properties of pure states with respect to this splitting. In this context we show that the amount of entanglement contained in a given state is deeply related to the von Neumann type of the observable algebras associated to the half-chains. Only the type I case belongs to the usual entanglement theory which deals with density operators on tensor product Hilbert spaces, and only in this situation separable normal states exist. In all other cases the corresponding state is infinitely entangled in the sense that one copy of the system in such a state is sufficient to distill an infinite amount of maximally entangled qubit pairs. We apply this results to the critical XY model and show that its unique ground state provides a particular example for this type of entanglement.