|
The AKLT model is an extension of the one-dimensional quantum Heisenberg spin model. The proposal and exact solution of this model by Affleck, Lieb, Kennedy and Tasaki〔 provided crucial insight into the physics of the spin-1 Heisenberg chain.〔 F. D. M. Haldane, Phys. Rev. Lett. 50, 1153 (1983), Phys. Lett. A 93, 464 (1983); I. Affleck and F. D. M. Haldane, Phys. Rev. B 36, 5291 (1987); I. Affleck, J. Phys.: Condens. Matter. 1, 3047 (1989). 〕 It has also served as a useful example for such concepts as valence bond solid order, symmetry protected topological order〔 Zheng-Cheng Gu and Xiao-Gang Wen (Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order ) Phys. Rev. B80, 155131 (2009). 〕〔〔Xie Chen, Zheng-Cheng Gu, Xiao-Gang Wen, (Classification of Gapped Symmetric Phases in 1D Spin Systems ) ''Phys. Rev. B'' 83, 035107 (2011); Xie Chen, Zheng-Xin Liu, Xiao-Gang Wen, (2D symmetry protected topological orders and their protected gapless edge excitations ) ''Phys. Rev. B'' 84, 235141 (2011)〕 and matrix product state wavefunctions. == Background == A major motivation for the AKLT model was the Majumdar–Ghosh chain. Because two out of every set of three neighboring spins in a Majumdar–Ghosh ground state are paired into a singlet, or valence bond, the three spins together can never be found to be in a spin 3/2 state. In fact, the Majumdar–Ghosh Hamiltonian is nothing but the sum of all projectors of three neighboring spins onto a 3/2 state. The main insight of the AKLT paper was that this construction could be generalized to obtain exactly solvable models for spin sizes other than 1/2. Just as one end of a valence bond is a spin 1/2, the ends of two valence bonds can be combined into a spin 1, three into a spin 3/2, etc. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「AKLT model」の詳細全文を読む スポンサード リンク
|