一般场下XYZ自旋系统的因式分解和可分基态工程
Factorization in XYZ spin systems under general fields and separable ground state engineering
摘要：
我们讨论一般磁场下，不一定是均匀或横向的$XYZ$耦合自旋$S$阵列的基态分解方案。它首先示出，给定任意的自旋取向方向在每个站点，非零耦合之间的任何对和字段在每个站点总是存在的，这样，随后的哈密顿量有一个完全可分离的本征态的自旋指向沿指定的方向。此外，通过适当的场调谐，本征态总是可以冷却到非简并基态。它还表明，在开放的一维系统与任意的$XYZ$第一邻居耦合，至少有一个可分离的本征态兼容的任意选择的自旋方向在一个网站总是可行的，如果在每个网站的领域可以调整。我们还证明，在因子分解附近，即，对于场或耦合中的小扰动，成对纠缠达到全范围。一些值得注意的例子的因式分解本征态的均匀耦合。这些结果为可分离的基态工程开辟了道路。一个符号来量化的复杂性，根据所需的控制系统的耦合和字段的一个给定类型的解决方案。
英文摘要：
We discuss ground state factorization schemes in spin $S$ arrays with general $XYZ$ couplings under general magnetic fields, not necessarily uniform or transverse. It is first shown that given arbitrary spin alignment directions at each site, nonzero couplings between any pair and fields at each site always exist such that the ensuing Hamiltonian has an exactly separable eigenstate with the spins pointing along the specified directions. Furthermore, by suitable tuning of the fields this eigenstate can always be cooled down to a nondegenerate ground state. It is also shown that in open one-dimensional systems with arbitrary $XYZ$ first neighbor couplings, at least one separable eigenstate compatible with an arbitrarily chosen spin direction at one site is always feasible if the fields at each site can be tuned. We demonstrate as well that in the vicinity of factorization, i.e., for small perturbations in the fields or couplings, pairwise entanglement reaches full range. Some noticeable examples of factorized eigenstates for uniform couplings are unveiled. The present results open the way for separable ground state engineering. A notation to quantify the complexity of a given type of solution according to the required control on the system couplings and fields is introduced.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
