USING DISCRETE VARIABLE REPRESENTATION PATH INTEGRAL MONTE CARLO WITH METROPOLIS SAMPLING TO COMPUTE GROUND STATE WAVEFUNCTIONS

Abstract

The discrete variable representation (DVR) matrix dynamics formulation of the path integral Monte Carlo (PIMC) method, implemented numerically in a way that enables Metropolis sampling to be employed, is proposed as a means of computing ground state quantum wavefunctions. A key advantage of the DVR-PIMC approach is that customized marginal potentials may be employed, leading to significantly larger PIMC time step sizes, and substantial reductions in computational (CPU) effort. An additional key advantage of the present implementation is that the DVR provides a natural set of interpolant functions that can be used for accurate interpolation and extrapolation of function and tensor quantities away from predefined grid points. The new method is applied here to compute the ground state wavefunction of a model one degree-of-freedom (1 DOF) Morse oscillator system. A one-to-two order-of-magnitude reduction in CPU effort is observed, in comparison with a conventional PIMC simulation. The generalization for many DOFs is straightforward, and expected to result in even greater performance enhancement.