# The topological basis realization and the corresponding Heisenberg model of spin-1 chain

The topological basis realization and the corresponding Heisenberg model of spin-1 chain In this paper, it is shown that the Heisenberg model of spin-1 chain can be constructed from the Birman–Wenzl algebra generator while we have got that the Heisenberg model of spin- $$\frac{1}{2}$$ 1 2 chain can be constructed from the Temperley–Lieb algebra generator in our previous work (Sun et al. in EPL 94:50001, 2011). Here, we investigate the topological space, we find that the number of topological basis states raise from the previous two to three, and they are also the three eigenstates of a closed four-qubit Heisenberg model of spin-1 chain. Specifically, all the topological basis states are also the spin single states and one of them is the energy single state of the system. It is worth noting that all conclusions we get in this paper are consistent with our previous work (Sun et al. in EPL 94:50001, 2011). These just indicate that the topological basis states have particular properties in the system. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# The topological basis realization and the corresponding Heisenberg model of spin-1 chain

, Volume 13 (2) – Oct 19, 2013
10 pages

/lp/springer_journal/the-topological-basis-realization-and-the-corresponding-heisenberg-EN0zHtAXi7
Publisher
Springer US
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/s11128-013-0648-z
Publisher site
See Article on Publisher Site

### Abstract

In this paper, it is shown that the Heisenberg model of spin-1 chain can be constructed from the Birman–Wenzl algebra generator while we have got that the Heisenberg model of spin- $$\frac{1}{2}$$ 1 2 chain can be constructed from the Temperley–Lieb algebra generator in our previous work (Sun et al. in EPL 94:50001, 2011). Here, we investigate the topological space, we find that the number of topological basis states raise from the previous two to three, and they are also the three eigenstates of a closed four-qubit Heisenberg model of spin-1 chain. Specifically, all the topological basis states are also the spin single states and one of them is the energy single state of the system. It is worth noting that all conclusions we get in this paper are consistent with our previous work (Sun et al. in EPL 94:50001, 2011). These just indicate that the topological basis states have particular properties in the system.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 19, 2013

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