Guided random walks for solving Hamiltonian lattice gauge theories

Motivated by developments for many-particle quantum systems, a Monte Carlo method for solving Hamiltonian lattice gauge theories without fermions is presented in which a stochastic random walk is guided by a trial wave function. To the extent that a substantial portion of the local structure of the theory can be incorporated in the trial function, the method offers significant advantages relative to existing techniques. The method is applicable to the study of SU(N) lattice gauge theories, and its utility is demonstrated by solving the compact U(1) gauge theory in three spatial dimensions.