Sparse modeling of large-scale quantum impurity models with low symmetries
Sparse modeling of large-scale quantum impurity models with low symmetries
复制标题
低对称性大规模量子杂质模型的稀疏建模
DOI：
10.1103/physrevb.103.045120
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发表时间：
2021
影响因子：
3.7
通讯作者：
Nagai Yuki
中科院分区：
文献类型：
--
作者：
Shinaoka Hiroshi;Nagai Yuki
量子嵌入理论可用于获得相关材料的定量描述。然而，一个关键的挑战是解决嵌入电子浴中的相关轨道的有效杂质模型。许多先进的杂质求解器需要使用有限数量的浴水平来近似浴连续体，从而产生高度非凸的病态逆问题。为了解决这个缺点，本研究提出了一种基于数据科学方法、稀疏建模和松原格林函数的紧凑表示的矩阵值杂交函数的有效拟合算法。该方法的效率通过在低温下拟合具有大非对角元素的随机杂化函数和高化合物 LaAsFeO 的 20 轨道杂质模型的随机杂化函数来证明。研究结果为复杂相关材料的量子嵌入模拟的杂质求解器的未来发展设定了定量目标。
Quantum embedding theories can be used for obtaining quantitative descriptions of correlated materials. However, a critical challenge is solving an effective impurity model of correlated orbitals embedded in an electron bath. Many advanced impurity solvers require the approximation of a bath continuum using a finite number of bath levels, producing a highly nonconvex, ill-conditioned inverse problem. To address this drawback, this study proposes an efficient fitting algorithm for matrix-valued hybridization functions based on a data-science approach, sparse modeling, and a compact representation of Matsubara Green's functions. The efficiency of the proposed method is demonstrated by fitting random hybridization functions with large off-diagonal elements and those of a 20-orbital impurity model for a high-compound, LaAsFeO, at low temperatures. The results set quantitative goals for the future development of impurity solvers toward quantum embedding simulations of complex correlated materials.