scholarly journals ON HAAG DUALITY FOR PURE STATES OF QUANTUM SPIN CHAINS

2008 ◽  
Vol 20 (06) ◽  
pp. 707-724 ◽  
Author(s):  
M. KEYL ◽  
TAKU MATSUI ◽  
D. SCHLINGEMANN ◽  
R. F. WERNER
Keyword(s):  
Von Neumann Algebra ◽  
Quantum Spin ◽  
Spin Chains ◽  
Type I ◽  
Quantum Spin Chains ◽  
Haag Duality ◽  
Von Neumann ◽  
Infinite Intervals ◽  
Pure States

In this note, we consider quantum spin chains and their translationally invariant pure states. We prove Haag duality for quasilocal observables localized in semi-infinite intervals (-∞ , 0] and [1, ∞) when the von Neumann algebra generated by observables localized in [0, ∞) is non-type I.

scholarly journals ENTANGLEMENT, HAAG-DUALITY AND TYPE PROPERTIES OF INFINITE QUANTUM SPIN CHAINS

2006 ◽  
Vol 18 (09) ◽  
pp. 935-970 ◽  
Author(s):  
M. KEYL ◽  
T. MATSUI ◽  
D. SCHLINGEMANN ◽  
R. F. WERNER
Keyword(s):  
Hilbert Spaces ◽  
Quantum Spin ◽  
Xy Model ◽  
Type I ◽  
Quantum Spin Chains ◽  
Haag Duality ◽  
Von Neumann ◽  
Neumann Type ◽  
Left And Right ◽  
Normal States

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.

Abundance of translation invariant pure states on quantum spin chains

1992 ◽  
Vol 25 (3) ◽  
pp. 249-258 ◽  
Author(s):  
M. Fannes ◽  
B. Nachtergaele ◽  
R. F. Werner
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Translation Invariant ◽  
Pure States

Solvable nineteen-vertex models and quantum spin chains of spin one

1994 ◽  
Vol 4 (8) ◽  
pp. 1151-1159 ◽  
Author(s):  
Makoto Idzumi ◽  
Tetsuji Tokihiro ◽  
Masao Arai
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Vertex Models

scholarly journals Long-lived Néel states in antiferromagnetic quantum spin chains with strong uniaxial anisotropy for atomic-scale antiferromagnetic spintronics

RSC Advances ◽  
2015 ◽  
Vol 5 (129) ◽  
pp. 106333-106338 ◽  
Author(s):  
Jun Li ◽  
Bang-Gui Liu
Keyword(s):  
Uniaxial Anisotropy ◽  
Life Time ◽  
Quantum Spin ◽  
Spin Chains ◽  
Atomic Scale ◽  
Quantum Spin Chains ◽  
Long Life

We achieve a powerful life-time expression of the Neel states for arbitrary parameters and show that for famous Fe adatom chains on Cu2N surface, 14 or 16 Fe adatoms are enough to obtain a long life-time for Neel state storage of information.

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