A Bayesian analysis of Green’s function Monte Carlo correlation functions

1992 ◽  
Vol 97 (11) ◽  
pp. 8415-8423 ◽  
Author(s):  
M. Caffarel ◽  
D. M. Ceperley
Keyword(s):  
Monte Carlo ◽  
Bayesian Analysis ◽  
Green’S Function ◽  
Green's Function ◽  
Correlation Functions ◽  
Green's Function Monte Carlo

scholarly journals The Use of Parameter-Free Correlation Functions in Green's Function Monte Carlo Simulations of Small Electronic Systems

1997 ◽  
Vol 52 (11) ◽  
pp. 793-802 ◽  
Author(s):  
C. Mecke ◽  
F. F. Seelig
Keyword(s):  
Monte Carlo ◽  
Green’S Function ◽  
Green's Function ◽  
Correlation Functions ◽  
High Performance ◽  
Limited Range ◽  
Electronic Energy ◽  
Simple Expression ◽  
Electronic Systems ◽  
Green's Function Monte Carlo

Abstract Using an old formulation for correlation functions with correct cusp-behaviour, the Schrödinger equation transforms to a new differential equation which provides a very simple expression for the local electronic energy with limited range. This, together with the simplicity of the formulation promises a high performance in Green's function Monte Carlo (GFMC) simulations of small electronic systems. The behaviour of the local energy is studied on a few simple examples because the variance of this function determines the quality of the results in the GFMC methods. Calculations for one-and two-electron systems are presented and compared with results from well-known functions. The form of the function is then extended to systems with more than two electrons. Results for the Be atom are given and the extension to larger electronic systems is discussed.

scholarly journals Forward-walking Green's Function Monte Carlo Method for Correlation Functions

1999 ◽  
Vol 52 (4) ◽  
pp. 637 ◽  
Author(s):  
M. Samaras ◽  
C. J. Hamer
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Green’S Function ◽  
Green's Function ◽  
Correlation Functions ◽  
Exact Results ◽  
Expectation Values ◽  
Trial Wavefunction ◽  
Local Observables ◽  
Green's Function Monte Carlo

The forward-walking Green's Function Monte Carlo method is used to compute expectation values for the transverse Ising model in (1 + 1)D, and the results are compared with exact values. The magnetisation Mz and the correlation function p z (n) are computed. The algorithm reproduces the exact results, and convergence for the correlation functions seems almost as rapid as for local observables such as the magnetisation. The results are found to be sensitive to the trial wavefunction, however, especially at the critical point.

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