Fast evaluation of multideterminant wavefunctions in quantum Monte Carlo

Quantum Monte Carlo (QMC) methods such as variational and diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multislater- Jastrow wave function which consists of a Jastrow function multiplied by the sum of slater determinants. In this talk we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient, and easily parallelized. The algorithm computes the multi determinant ratios of a series of particle hole excitations in time O(n$^{2})$+O(n$_{s}$n)+O(n$_{e})$ where n, n$_{s}$ and n$_{e}$ are the number of particles, single particle excitations, and total number of excitations, respectively. This is accomplished by producing a (relatively) compact table that contains all the information required to read off the excitation ratios. In addition we describe how to compute the gradients and laplacians of these multi determinant terms.