### Abstract

We consider an infinite spin chain as a bipartite system consisting of the left and right half-chains 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 φs provides a particular example for this type of entanglement.

Original language | English |
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Pages (from-to) | 935-970 |

Number of pages | 36 |

Journal | Reviews in Mathematical Physics |

Volume | 18 |

Issue number | 9 |

DOIs | |

Publication status | Published - Oct 1 2006 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Reviews in Mathematical Physics*,

*18*(9), 935-970. https://doi.org/10.1142/S0129055X0600284X