We consider the problem of extracting an effective low-energy spin model from a Kondo Lattice Model (KLM) with classical localized moments. The non-analytic dependence of the effective spin-spin interactions on the Kondo exchange $J$ excludes the possibility of using perturbation theory beyond the second order Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction at zero temperature. Here we introduce a Machine Learning (ML) assisted protocol to extract effective two- and four-spin interactions by integrating out the conduction electrons of the original KLM. The resulting effective spin model reproduces the phase diagram obtained with the original KLM as a function of magnetic field and easy-axis anisotropy and reveals the effective four-spin interactions that are responsible for the field induced skyrmion crystal phase. Moreover, this minimal spin model enables an efficient computation of static and dynamical properties with a much lower numerical cost relative to the original KLM. A comparison of the dynamical spin structure factor in the fully polarized phase computed with the effective model and the original KLM reveals a good agreement for the magnon dispersion despite the fact that this information was not included in the training data set.
Exciton-assisted low-energy magnetic excitations in a photoexcited Mott insulator on a square lattice
正方形晶格上的莫特绝缘体的光激发减弱了时间分辨共振非弹性X射线散射和时间分辨拉曼散射中分别观察到的单磁振子和双磁振子激发的强度。然而，磁振子下方低能区的光谱变化还没有被清楚地理解。为了揭示莫特绝缘体光生低能磁激发的本质，我们数值研究了正方晶格上光激发半填充哈伯德模型的瞬态磁动力学.在关闭一个吸收边调谐的泵浦脉冲后，新的磁信号明显地出现在单磁振子和双磁振子激发中的磁振子能量之下。我们发现，低能量激发主要是通过激子态的吸收边。这些激子辅助的磁激发可以提供一个可能的解释在最近的时间分辨的两个磁振子拉曼散射实验绝缘YBa $_2$ Cu $_3$ O $_{6.1}$的低能谱权重。
