Constrained path Monte Carlo method for fermion ground states

Shiwei Zhang, J. Carlson, and J. E. Gubernatis
Phys. Rev. B 55, 7464 – Published 15 March 1997
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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 overcomplete basis of Slater determinants. By constraining the determinants according to a trial wave function |ψT〉, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if |ψT〉 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. With simple single-determinant wave functions as |ψT〉, the method yields accurate (often to within a few percent) estimates of the ground-state energy as well as correlation functions, such as those for electron pairing. We conclude by discussing possible extensions of the algorithm.

    DOI:https://doi.org/10.1103/PhysRevB.55.7464

    ©1997 American Physical Society

    Authors & Affiliations

    Shiwei Zhang

    • Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
    • and Department of Physics, The Ohio State University, Columbus, Ohio 43210

    J. Carlson and J. E. Gubernatis

    • Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

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    Vol. 55, Iss. 12 — 15 March 1997

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