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

M. Keyl, T. Matsui, D. Schlingemann, R. F. Werner

研究成果: ジャーナルへの寄稿記事

18 引用 (Scopus)

抄録

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.

元の言語英語
ページ(範囲)935-970
ページ数36
ジャーナルReviews in Mathematical Physics
18
発行部数9
DOI
出版物ステータス出版済み - 10 1 2006

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Quantum Spin Chain
Entanglement
Duality
Hilbert space
Density Operator
XY Model
Spin Chains
Pure State
algebra
Qubit
tensors
Tensor Product
Ground State
operators
ground state
products
Sufficient
Algebra

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

これを引用

Entanglement, haag-duality and type properties of infinite quantum spin chains. / Keyl, M.; Matsui, T.; Schlingemann, D.; Werner, R. F.

:: Reviews in Mathematical Physics, 巻 18, 番号 9, 01.10.2006, p. 935-970.

研究成果: ジャーナルへの寄稿記事

Keyl, M. ; Matsui, T. ; Schlingemann, D. ; Werner, R. F. / Entanglement, haag-duality and type properties of infinite quantum spin chains. :: Reviews in Mathematical Physics. 2006 ; 巻 18, 番号 9. pp. 935-970.
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