论文标题
建立特征向量和矩阵元素之间的简单关系
Establishing simple relationship between eigenvector and matrix elements
论文作者
论文摘要
为具有非阳性非偏离元件的真实对称矩阵建立了基层特征向量与每行矩阵元素的总和之间的简单近似关系。具体而言，地基州特征向量的$ i $ th组件可以由$（-S_I）^p+c $计算，其中$ s_i $是矩阵的$ i $ th行中$ p $和$ c $是变量参数的元素的总和。简单的关系提供了一种直接计算矩阵基态特征向量的直接方法。我们对Hubbard模型的初步应用和横向场中的ISING模型表现出令人鼓舞的结果。简单的关系还为其他更准确的方法（例如Lanczos方法）提供了最佳的初始状态。
A simple approximate relationship between the ground-state eigenvector and the sum of matrix elements in each row has been established for real symmetric matrices with non-positive off-diagonal elements. Specifically, the $i$-th components of the ground-state eigenvector could be calculated by $(-S_i)^p+c$, where $S_i$ is the sum of elements in the $i$-th row of the matrix with $p$ and $c$ being variational parameters. The simple relationship provides a straightforward method to directly calculate the ground-state eigenvector for a matrix. Our preliminary applications to the Hubbard model and the Ising model in a transverse field show encouraging results.The simple relationship also provide the optimal initial state for other more accurate methods, such as the Lanczos method.
