标题： 代数解用于$SU(2)\otimes SU(2)$哈密顿本征系统：通用统计系综和介观系统应用 显示英文标题

标题： Algebraic solutions for $SU(2)\otimes SU(2)$ Hamiltonian eigensystems: generic statistical ensembles and a mesoscopic system application

摘要： 通过系统处理四次多项式方程，获得了通用$SU(2)\otimes SU(2)$哈密顿本征系统的解。 提出了一种{\em 假设}，用于根据四次方程的系数构造可分离和纠缠本征态基。 除了纯纠缠态的量子并发性外，相关的热力学统计系综、其配分函数、量子纯度和量子并发性也被证明可以直接获得。 结果专门应用于由伯纳尔堆叠石墨烯的晶格层自由度模拟的$SU(2)\otimes SU(2)$结构，在这一背景下，可以扩展到多个介观尺度系统，这些系统假设起始于$SU(2)\otimes SU(2)$哈密顿量。 显示英文摘要

摘要： Solutions of generic $SU(2)\otimes SU(2)$ Hamiltonian eigensystems are obtained through systematic manipulations of quartic polynomial equations. An {\em ansatz} for constructing separable and entangled eigenstate basis, depending on the quartic equation coefficients, is proposed. Besides the quantum concurrence for pure entangled states, the associated thermodynamic statistical ensembles, their partition function, quantum purity and quantum concurrence are shown to be straightforwardly obtained. Results are specialized to a $SU(2)\otimes SU(2)$ structure emulated by lattice-layer degrees of freedom of the Bernal stacked graphene, in a context that can be extended to several mesoscopic scale systems for which the onset from $SU(2)\otimes SU(2)$ Hamiltonians has been assumed.