Volume 122, Number 5, June 2018
|Number of page(s)||5|
|Published online||18 July 2018|
Topological basis realization associated with Hermitian and non-Hermitian Heisenberg XXZ model
Center for Quantum Sciences and School of Physics, Northeast Normal University - Changchun 130024, China
Received: 29 April 2018
Accepted: 21 June 2018
We investigate the topological basis realization associated with the Hermitian and non-Hermitian Heisenberg XXZ model based on the matrix representation of the Temperley-Lieb algebra. The results show that the topological space is spanned by the topological basis associated with the Temperley-Lieb algebra. When the q-deformed parameter q is a complex number and , the corresponding model is the non-Hermitian XXZ model. The real q corresponds to the Hermitan case. The topological basis realization for these two cases is constructed by means of matrix representation of the Temperley-Lieb algebra. Then the properties of the topological basis and ground state are studied. Particularly, the four-qubit Heisenberg XXZ model is investigated in detail. We also give some discussions on the case in which q is a root of unity.
PACS: 03.65.Fd – Algebraic methods / 02.10.Kn – Knot theory / 75.10.Jm – Quantized spin models, including quantum spin frustration
© EPLA, 2018
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