TY - JOUR

T1 - The simulation of quantum systems with random walks

T2 - A new algorithm for charged systems

AU - Ceperley, D.

N1 - Funding Information:
The authort hanksD r. E. L. Pollock for many fruitfuld iscussionso n the Coulomb densitym atrix and for suggestionsc oncerningt his manuscript.T his work was performedu nder the auspiceso f the U. S. Department of Energy by the Lawrence Livermore National Laboratory under contract No. W-7405~ENG-48.

PY - 1983/9

Y1 - 1983/9

N2 - Random walks with branching have been used to calculate exact properties of the ground state of quantum many-body systems. In this paper, a more general Green's function identity is derived which relates the potential energy, a trial wavefunction, and a trial density matrix to the rules of a branched random walk. It is shown that an efficient algorithm requires a good trial wavefunction, a good trial density matrix, and a good sampling of this density matrix. An accurate density matrix is constructed for Coulomb systems using the path integral formula. The random walks from this new algorithm diffuse through phase space an order of magnitude faster than the previous Green's Function Monte Carlo method. In contrast to the simple diffusion Monte Carlo algorithm, it is an exact method. Representative results are presented for several molecules.

AB - Random walks with branching have been used to calculate exact properties of the ground state of quantum many-body systems. In this paper, a more general Green's function identity is derived which relates the potential energy, a trial wavefunction, and a trial density matrix to the rules of a branched random walk. It is shown that an efficient algorithm requires a good trial wavefunction, a good trial density matrix, and a good sampling of this density matrix. An accurate density matrix is constructed for Coulomb systems using the path integral formula. The random walks from this new algorithm diffuse through phase space an order of magnitude faster than the previous Green's Function Monte Carlo method. In contrast to the simple diffusion Monte Carlo algorithm, it is an exact method. Representative results are presented for several molecules.

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U2 - 10.1016/0021-9991(83)90161-4

DO - 10.1016/0021-9991(83)90161-4

M3 - Article

AN - SCOPUS:0005368660

VL - 51

SP - 404

EP - 422

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 3

ER -