Proof for an upper bound in fixed-node Monte Carlo for lattice fermions

TL;DR

This paper justifies and generalizes a Green Function Monte Carlo method for lattice fermions, providing an upper bound for ground-state energy and demonstrating its effectiveness on small systems.

Contribution

It proves that the effective Hamiltonian used in the method yields an upper bound for the true ground-state energy and extends the method to systems with various hopping term signs.

Findings

The method avoids the sign problem in lattice fermion simulations.

The effective Hamiltonian provides an upper bound for the ground-state energy.

The approach is effective on small lattice systems.

Abstract

We justify a recently proposed prescription for performing Green Function Monte Carlo calculations on systems of lattice fermions, by which one is able to avoid the sign problem. We generalize the prescription such that it can also be used for problems with hopping terms of different signs. We prove that the effective Hamiltonian, used in this method, leads to an upper bound for the ground-state energy of the real Hamiltonian, and we illustrate the effectiveness of the method on small systems.