On the topological dual of the XXZ spin chain

Guijiao Du, Kang Xue, Chengcheng Zhou

Qingyong Wang, Yangyang Du, Chunfeng Wu +3 more

In this paper, it is shown that the Hamiltonian of the open spin-1 XXZ chain model can be constructed from the generators of the Birman–Murakami–Wenzl (B–M–W) algebra. Without the topological parameter d (describing the unknotted loop [Formula: see text] in topology) reducing to a fixed value, the topological basis states can be connected with the open XXZ spin chain. Then some particular properties of the topological basis states in this system have been investigated. We find that the topological basis states are the three eigenstates of a four-spin-1 XXZ chain model without boundary term. Specifically, all the spin single states of the system fall on the topological basis subspace. And the number of the spin single states of the system is equal to that of the topological basis states.

Feifei Wang, Yue Cao, Yizi Zhu +3 more

Бо Лю, Kang Xue, Gangcheng Wang +2 more

In this paper, we study three-dimensional (3D) reduced Birman–Murakami–Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.

Yasuhiro Fujii, Miki Wadati

The asymmetric XXZ chain is studied in the framework of the algebraic Bethe ansatz. The model is one of the Heisenberg XXZ spin chains with Dzyaloshinsky–Moriya interactions and is mapped onto the asymmetric six-vertex model. We calculate the scalar products that constitute various correlation functions of the model, by the Korepin's method. They are expressed in terms of determinants of the dual quantum fields.

Chi Shi