一般双线性哈密顿量的热结构因子与耦合常数的一一对应
One-to-one correspondence between thermal structure factors and coupling constants of general bilinear Hamiltonians
摘要：
最近，J. Quintanilla利用密度泛函理论中的Hohenberg-Kohn定理的思想建立了一个定理，该定理为自旋算符中的一般类量子自旋哈密顿量双线性建立了零温静态自旋-自旋算符与耦合常数之间的一对一关系。Quintanilla定理为利用自旋结构因子作为输入数据的量子自旋哈密顿学习提供了坚实的理论基础。在这里，我们在两个方向上扩展定理的有效性。首先，按照与Mermin相同的方法，证明被扩展到有限温度自旋结构因子的情况下，从而确保该定理对实验数据的应用是合理的。其次，我们注意到这个定理适用于所有类型的哈密顿量表示为双线性算子的总和，所以它也可以联系的密度-密度算符的库仑矩阵元的相互作用的电子在最低的朗道水平。
英文摘要：
A theorem that establishes a one-to-one relation between zero-temperature static spin-spin correlators and coupling constants for a general class of quantum spin Hamiltonians bilinear in the spin operators has been recently established by J. Quintanilla, using an argument in the spirit of the Hohenberg-Kohn theorem in density functional theory. Quintanilla's theorem gives a firm theoretical foundation to quantum spin Hamiltonian learning using spin structure factors as input data. Here we extend the validity of the theorem in two directions. First, following the same approach as Mermin, the proof is extended to the case of finite-temperature spin structure factors, thus ensuring that the application of this theorem to experimental data is sound. Second, we note that this theorem applies to all types of Hamiltonians expressed as sums of bilinear operators, so that it can also relate the density-density correlators to the Coulomb matrix elements for interacting electrons in the lowest Landau level.
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。
