Exact solution of a cluster model with next-nearest-neighbor interaction
Exact solution of a cluster model with next-nearest-neighbor interaction
复制标题
DOI：
10.1093/ptep/ptaa146
复制
发表时间：
2020-03
影响因子：
3.5
通讯作者：
Yuji Yanagihara;K. Minami
中科院分区：
文献类型：
--
作者：
Yuji Yanagihara;K. Minami
求解了具有次近邻相互作用和两个附加复合相互作用的一维团簇模型，得到了自由能，并精确地导出了关联函数。该模型通过由其相互作用自动获得的变换对角化，该变换是Jordan-Wigner变换的代数推广。将无间隙条件表示为三次方程的根上的条件，得到了精确的相图。我们发现，这个代数方程的根的分布决定了长程有序的存在，并再次得到了基态相图。我们还导出了相应的共形场论的中心电荷。最后，我们注意到我们的结果对无限多个相互作用遵循相同代数关系的可解自旋链普遍有效。
A 1D cluster model with next-nearest-neighbor interactions and two additional composite interactions is solved; the free energy is obtained and a correlation function is derived exactly. The model is diagonalized by a transformation obtained automatically from its interactions, which is an algebraic generalization of the Jordan–Wigner transformation. The gapless condition is expressed as a condition on the roots of a cubic equation, and the phase diagram is obtained exactly. We find that the distribution of roots for this algebraic equation determines the existence of long-range order, and we again obtain the ground-state phase diagram. We also derive the central charges of the corresponding conformal field theory. Finally, we note that our results are universally valid for an infinite number of solvable spin chains whose interactions obey the same algebraic relations.