A method for calculating the eigenvalues of large Hermitian matrices by second-order recursion formulae Original Research Article

A general discussion of a method for solving the eigenvalue problem of large N × N Hermitian matrices by using second-order recursion formulae is given. In principle, the method is suitable for finding not only the extreme eigenvalues and the corresponding eigenvectors but also any other eigenvalues in the range of oneʹs specification. The effectiveness of the algorithm is illustrated by calculation of a few low-lying eigenvalues of the Heisenberg model for an antiferromagnetic chain with N up to 1048576.