A New Approach to Stochastic State Selections in Quantum Spin Systems

Abstract

We propose a new type of Monte Carlo approach in numerical studies of quantum systems. Introducing a probability function which determines whether a state in the vector space survives or not, we can evaluate expectation values of powers of the Hamiltonian from a small portion of the full vector space. This method is free from the negative sign problem because it is not based on importance sampling techniques. In this paper we describe our method and, in order to examine how effective it is, present numerical results on the 4×4, 6×6 and 8×8 Heisenberg spin one-half model. The results indicate that we can perform useful evaluations with limited computer resources. An attempt to estimate the lowest energy eigenvalue is also stated.