Exact solution of Heisenberg model with site-dependent exchange couplings and Dzyloshinsky–Moriya interaction**Project supported by the National Natural Science Foundation of China (Grant Nos. 11174335, 11375141, 11374334, and 11434013) and the National Program for Basic Research of China and the Fund from the Chinese Academy of Sciences.

Abstract

We propose an integrable spin-1/2 Heisenberg model where the exchange couplings and Dzyloshinky–Moriya interactions are dependent on the sites. By employing the quantum inverse scattering method, we obtain the eigenvalues and the Bethe ansatz equation of the system with the periodic boundary condition. Furthermore, we obtain the exact solution and study the boundary effect of the system with the anti-periodic boundary condition via the off-diagonal Bethe ansatz. The operator identities of the transfer matrix at the inhomogeneous points are proved at the operator level. We construct the T–Q relation based on them. From which, we obtain the energy spectrum of the system. The corresponding eigenstates are also constructed. We find an interesting coherence state that is induced by the topological boundary.