A Constrained Path Monte Carlo Method for Fermion Ground States

1996/07/09 by Shiwei Zhang, J. Carlson, J. E. Gubernatis · 1 citation
Physics and Astronomy · #cond-mat #nucl-th

paper · pdf · doi:10.1103/physrevb.55.7464

published as Phys.Rev. B55 (1997) 7464 · 29 pages, RevTex, 3 figures included; submitted to Phys. Rev. B

arxiv created 1996/07/09 · arxiv updated 2009/11/30

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 |ψ_T⟩, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if |ψ_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× 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.

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