# The quantum spin chains of Temperley–Lieb type and the topological basis states

The quantum spin chains of Temperley–Lieb type and the topological basis states In this paper, based on the usual spin basis, we present a complete orthonormal basis with the single loop $$d=\sqrt{2}$$ consisting of maximally entangled four-qubit states. Then we investigate the particular physical properties of the topological basis states in the corresponding quantum spin chains of Temperley–Lieb type. Whether the system is the anti-ferromagnetic case or the ferromagnetic case, the ground states are all doubly degenerate, and they all fall on the topological basis states. Furthermore, we introduce the Yangian $$Y(sl(2))$$ operators to investigate the transitions between the quantum states. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# The quantum spin chains of Temperley–Lieb type and the topological basis states

, Volume 12 (9) – May 12, 2013
14 pages

/lp/springer_journal/the-quantum-spin-chains-of-temperley-lieb-type-and-the-topological-20UTIgvxPN
Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-013-0542-8
Publisher site
See Article on Publisher Site

### Abstract

In this paper, based on the usual spin basis, we present a complete orthonormal basis with the single loop $$d=\sqrt{2}$$ consisting of maximally entangled four-qubit states. Then we investigate the particular physical properties of the topological basis states in the corresponding quantum spin chains of Temperley–Lieb type. Whether the system is the anti-ferromagnetic case or the ferromagnetic case, the ground states are all doubly degenerate, and they all fall on the topological basis states. Furthermore, we introduce the Yangian $$Y(sl(2))$$ operators to investigate the transitions between the quantum states.

### Journal

Quantum Information ProcessingSpringer Journals

Published: May 12, 2013

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