We present a general formulation of the Green’s function Monte Carlo method in imaginary-time quantum Monte Carlo which employs exact propagators. This algorithm has no time-step errors and is obtained by minimal modifications of the time-independent Green’s function Monte Carlo method. We describe how the method can be applied to the many-body Schrödinger equation, lattice Hamiltonians, and simple field theories. Our modification of the Green’s function Monte Carlo algorithm is applied to the ground state of liquid ${}^4\mathrm{He}.$ We calculate the zero-temperature imaginary-time diffusion constant and relate that to the effective mass of a mass-four “impurity” atom in liquid ${}^4\mathrm{He}.$

• Received 19 December 2001

DOI:https://doi.org/10.1103/PhysRevE.71.016707