Quantum Monte Carlo with coupled-cluster wave functions

We introduce a many-body method that combines two powerful many-body techniques, viz., quantum Monte Carlo and coupled cluster theory. Coupled cluster wave functions are introduced as importance functions in a Monte Carlo method designed for the configuration interaction framework to provide rigorous upper bounds to the ground-state energy. We benchmark our method on the homogeneous electron gas in momentum space. The importance function used is the coupled cluster doubles wave function. We show that the computational resources required in our method scale polynomially with system size. Our energy upper bounds are in very good agreement with previous calculations of similar accuracy, and they can be systematically improved by including higher order excitations in the coupled cluster wave function.

Figure 1

Correlation energies for $N=14$ and $r_s=0.5,1.0,2.0$, and $3.0$ as a function of the single particle basis size from CIMC with the CCD(1) importance function. The statistical errors are smaller than the size of the symbols. The lines are drawn as a guide to the eye.