Establishing simple relationship between eigenvector and matrix elements
arXiv:2003.13396 · doi:10.1016/j.physleta.2020.126610
Abstract
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 -th components of the ground-state eigenvector could be calculated by , where is the sum of elements in the -th row of the matrix with and 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.
arXiv comment17 pages, 7 figures
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