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Chin. Phys. B, 2015, Vol. 24(10): 107502    DOI: 10.1088/1674-1056/24/10/107502

Exact solution of Heisenberg model with site-dependent exchange couplings and Dzyloshinsky-Moriya interaction

Yang Li-Jun (杨丽君)a, Cao Jun-Peng (曹俊鹏)a b, Yang Wen-Li (杨文力)c d
a Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
b Collaborative Innovation Center of Quantum Matter, Beijing, China;
c Institute of Modern Physics, Northwest University, Xian 710069, China;
d Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing 100048, China

We propose an integrable spin-1/2Heisenberg 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.

Keywords:  Bethe ansatz      Yang-Baxter equation      T-Q relation  
Received:  08 June 2015      Revised:  08 July 2015      Accepted manuscript online: 
PACS:  75.10.Pq (Spin chain models)  
  03.65.Vf (Phases: geometric; dynamic or topological)  
  71.10.Pm (Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.))  

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.

Corresponding Authors:  Yang Li-Jun     E-mail:

Cite this article: 

Yang Li-Jun (杨丽君), Cao Jun-Peng (曹俊鹏), Yang Wen-Li (杨文力) Exact solution of Heisenberg model with site-dependent exchange couplings and Dzyloshinsky-Moriya interaction 2015 Chin. Phys. B 24 107502

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