## UC Berkeley / Lawrence Berkeley Laboratory

#### Exact Coulomb Propagators for Green's Function Monte Carlo

**Ethan Atkins, UC Berkeley / LBL**

##### September 28th, 2011 at 4PM–5PM in 939 Evans Hall [Map]

Quantum Monte Carlo (QMC) refers to a set of stochastic algorithms that
evaluate quantitative properties of a quantum mechanical system, most typically
the ground-state energy.

Random walk methods, most notably diffusion Monte Carlo (DMC) and Green's
function Monte Carlo (GFMC), estimate the ground state by taking an ensemble of
random walkers and propagating them in time so that the invariant distribution
of walkers is the ground state. These algorithms generate correlated sequences
of random walkers, often requiring many steps of the algorithm to obtain
statistically independent samples. The average time step of GFMC can become
small due to the singularities in the potential.

I will show that by explicitly accounting for the local Coulomb potential,
one can achieve significantly larger mean time steps. The resulting algorithm
will be applied to the Helium (He) and Hydrogen (H_{2}) atoms,
achieving high accuracy and good speedup.