Exact Monte Carlo for few-fermion systems

U. Helmbrecht, John G. Zabolitzky

Carol A. Traynor

I. Morgenstern, Diethelm W�rtz

David M. Arnow, Malvin H. Kalos, Michael A. Lee +1 more

The Green’s function Monte Carlo method used for obtaining exact solutions to the Schrödinger equation of boson systems is generalized to treat systems of several fermions. We show that when it is possible to select eigenfunctions of the Hamiltonian based on physical symmetries, the GFMC method can be used to yield the lowest energy state of that symmetry. In particular, the lowest totally antisymmetric eigenfunction, the fermion ground state, can be obtained. Calculations on several two- and three-body model problems show the method to be computationally feasible for few-body systems.

Malvin H. Kalos

Yuriy Mishchenko

We suggest an exact approach to help remedy the fermion sign problem in diffusion quantum Monte Carlo simulations. The approach is based on an explicit suppression of symmetric modes in the Schrödinger equation by means of a modified stochastic diffusion process (antisymmetric diffusion process). We introduce this algorithm and illustrate it on potential models in one dimension (1D) and show that there it solves the fermion sign problem exactly and converges to the lowest antisymmetric state of the system. Then, we discuss extensions of this approach to many-dimensional systems on examples of quantum oscillator in 2D-20D and a toy model of three and four fermions on harmonic strings in 2D and 3D. We show that in all these cases our method shows a performance comparable to that of a fixed-node approximation with an exact node.