STOCHASTIC DIAGONALIZATION

Conventional Quantum Monte Carlo methods, routinely used to compute properties of many-body quantum systems, often suffer from what has been termed 'minus-sip'' problems. These problems are shown to result from an elementary property of the Hamiltonian and the use of stochastic (Markovian) simulation methods to compute physical quantities. An importance sampling algorithm is presented to compute the smallest eigenvalue(s) and the corresponding eigenvector(s) of extremely large matrices. It can exploit the sparsity of the solution of the eigenvalue problem. A rigorous proof of the correctness of the algorithm is given. Important aspects of the implementation of the algorithm are discussed at length. Demonstration programs are included. The method is applied to the two-dimensional Hubbard model. The performance of the algorithm is studied in great detail, confirming the expectations based on the theoretical analysis of the algorithm. Results are presented for the smallest eigenvalue and the properties of the corresponding eigenvector of matrices of order up to 10(35) X 10(35).