We propose a data-driven technique to estimate the spin Hamiltonian, including uncertainty, from multiple physical quantities. Using our technique, an effective model of ${\mathrm{KCu}}_4{\mathrm{P}}_3{\mathrm{O}}_{12}$ is determined from the experimentally observed magnetic susceptibility and magnetization curves with various temperatures under high magnetic fields. An effective model, which is the quantum Heisenberg model on a zigzag chain with eight spins having $J_1=-8.54\pm 0.51\mathrm{meV}$, $J_2=-2.67\pm 1.13\mathrm{meV}$, $J_3=-3.90\pm 0.15\mathrm{meV}$, and $J_4=6.24\pm 0.95\mathrm{meV}$, describes these measured results well. These uncertainties are successfully determined by the noise estimation. The relations among the estimated magnetic interactions or physical quantities are also discussed. The obtained effective model is useful to predict hard-to-measure properties such as spin gap, spin configuration at the ground state, magnetic specific heat, and magnetic entropy.

中文翻译：

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自旋哈密顿量参数及其不确定性的数据驱动确定：之字形链化合物KCu4P3O12的情况

我们提出了一种数据驱动的技术来从多个物理量估计自旋哈密顿量，包括不确定性。使用我们的技术，有效的模型${\mathrm{铜铜}}_4{\mathrm{P}}_3{\mathrm{Ø}}_{12}$根据实验观察到的在高磁场下不同温度下的磁化率和磁化曲线确定。一个有效的模型，它是锯齿形链上具有八个自旋的量子海森堡模型${Ĵ}_{\mathrm{1个}}=-8.54\pm 0.51\mathrm{病毒}$， ${Ĵ}_2=-2.67\pm 1.13\mathrm{病毒}$， ${Ĵ}_3=-3.90\pm 0.15\mathrm{病毒}$和 ${Ĵ}_4=6.24\pm 0.95\mathrm{病毒}$，很好地描述了这些测量结果。这些不确定性通过噪声估计成功确定。还讨论了估计的磁相互作用或物理量之间的关系。获得的有效模型可用于预测难以测量的属性，例如自旋间隙，基态的自旋构型，磁比热和磁熵。