TY - JOUR

T1 - Entanglement, haag-duality and type properties of infinite quantum spin chains

AU - Keyl, M.

AU - Matsui, T.

AU - Schlingemann, D.

AU - Werner, R. F.

N1 - Funding Information:
This research of M. K. is partially supported by the Ministero Italiano dell’Università e della Ricerca (MIUR) through FIRB (bando 2001) and PRIN 2005 and that of T. M. by the Center of Excellence Program, Graduate School Mathematics, Kyushu University, Japan.

PY - 2006/10

Y1 - 2006/10

N2 - 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.

AB - 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.

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U2 - 10.1142/S0129055X0600284X

DO - 10.1142/S0129055X0600284X

M3 - Article

AN - SCOPUS:33751577362

SN - 0129-055X

VL - 18

SP - 935

EP - 970

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

IS - 9

ER -