An explicit construction for Q-operators of the finite XXZ spin chain with twisted boundary conditions is presented. The massless and the massive regimes are considered as well as the root of unity case. It is explained how these results yield an alternative expression for the trace function employed in the description of the correlation functions of the inhomogeneous XXZ model on the infinite lattice by Boos, Jimbo, Miwa, Smirnov and Takeyama.

arXiv:hep-th/0503130Journal of Physics A Mathematical and GeneralJul 13, 200531 citations

Quantum Information Processing

The topological basis expression of four-qubit XXZ spin chain with twist boundary condition

Guijiao Du, Kang Xue, Chengcheng Zhou, Chunfang Sun, Gangcheng Wang

Published Feb 8, 2013• 0 citations

Publisher

DOI: 10.1007/s11128-012-0523-3

Related papers

Yangian and Topological Basis Expressions of Two Types of XXZ Spin Chains

Guijiao Du, Kang Xue, Chengcheng Zhou

International Journal of Theoretical PhysicsMay 4, 20190 citations

Topological Basis Method for Four-Qubit Spin- 1 2 $\frac {1}{2}$ XXZ Heisenberg Chain with Dzyaloshinskii-Moriya InteractionTopological Basis Method for Four-Qubit Spin- 1 2 $\frac {1}{2}$ XXZ Heisenberg Chain with Dzyaloshinskii-Moriya Interaction

Бо Лю, Kang Xue, Gangcheng Wang

International Journal of Theoretical PhysicsDec 15, 20161 citation

The open XXZ spin chain model and the topological basis realization

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.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.

International Journal of Quantum InformationApr 1, 20161 citation

The topological basis expression of Heisenberg spin chain

Taotao Hu, Hang Ren, Kang Xue

Quantum Information ProcessingOct 31, 20132 citations

Correlation functions of the XXZ spin chain with the twisted boundary condition

Yi Qiao, Zhirong Xin, Xiaotian Xu +4 more

The scalar products, form factors, and correlation functions of the XXZ spin chain with a twisted (or antiperiodic) boundary condition are obtained based on the inhomogeneous T–Q relation and the Bethe states constructed via the off-diagonal Bethe ansatz. It is shown that the scalar product of two off-shell Bethe states, the form factors, and the two-point correlation functions can be expressed as the summation of certain determinants. The corresponding homogeneous limits are studied. The results are also checked by the numerical calculations.The scalar products, form factors, and correlation functions of the XXZ spin chain with a twisted (or antiperiodic) boundary condition are obtained based on the inhomogeneous T–Q relation and the Bethe states constructed via the off-diagonal Bethe ansatz. It is shown that the scalar product of two off-shell Bethe states, the form factors, and the two-point correlation functions can be expressed as the summation of certain determinants. The corresponding homogeneous limits are studied. The results are also checked by the numerical calculations.

arXiv:1901.09604Journal of Mathematical PhysicsMar 1, 20201 citation

A Q-operator identity for the correlation functions of the infinite XXZ spin-chain

Christian Korff

arXiv:hep-th/0503130Journal of Physics A Mathematical and GeneralJul 13, 200531 citations

Topological Basis Method for Four-Qubit Spin- 1 2

\frac {1}{2}

XXZ Heisenberg Chain with Dzyaloshinskii-Moriya Interaction