Variance minimization variational Monte Carlo method

We present a variational Monte Carlo (VMC) method that works equally well for the ground and the excited states of a quantum system. The method is based on the minimization of the variance of energy, as opposed to the energy itself in standard methods. As a test, it is applied to the investigation of the universal spectrum at the van der Waals length scale for two identical Bose atoms in a symmetric harmonic trap, with results compared to the basically exact results obtained from a multiscale quantum-defect theory\footnote{Y. Chen and B. Gao, cond-mat/0701384.}. Results for trapped few-atom systems\footnote{I. Khan and B. Gao, Phys. Rev. A \textbf{73}, 063619 (2006).} will also be presented.