Constrained path Monte Carlo method for fermion ground states

We describe and discuss a recently proposed quantum Monte Carlo algorithm to compute the ground-state properties of various systems of interacting fermions. In this method, the ground state is projected fi om an initial wave function by a branching random walk in an overcomplete basis of Slater determinants. By constraining the determinants according to a trial wave function \psi(T)], we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if \psi(T)] is exact. We illustrate the method by describing in detail its implementation for the two-dimensional one-hand Hubbard model. We show results for lattice sizes up to 16x16 and for various electron fillings and interaction strengths. With simple single-determinant wave functions as \psi(T)], the method yields accurate (often to within a few percent) estimates of the ground-state energy as well as correlation functions, such as those for electron pairing. We conclude by discussing possible extensions of the algorithm.