A Constrained Path Monte Carlo Method for Fermion Ground States

Abstract

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 from an initial wave function by a branching random walk in an over-complete 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-band Hubbard model. We show results for lattice sizes up to $16\times 16$ and for various electron fillings and interaction strengths. Besides highly accurate estimates of the ground-state energy, we find that the method also yields reliable estimates of other ground-state observables, such as superconducting pairing correlation functions. We conclude by discussing possible extensions of the algorithm.

Comments: 29 pages, RevTex, 3 figures included; submitted to Phys. Rev. B