Variational Monte Carlo trial wavefunctions

Variational Monte Carlo (or VMC, as it is now commonly called) is a method that allows one to calculate quantum expectation values given a trial wavefunction [1,2]. The actual Monte Carlo methodology used for this is almost identical to the usual classical Monte Carlo methods, particularly those of statistical mechanics. Nevertheless, quantum behavior can be studied with this technique. The key idea, as in classical statistical mechanics, is the ability to write the desired property <0> of a system as an average over an ensemble... 

In variational Monte Carlo (VMC), one samples, using the Metropolis rejection method, the square of an assumed trial wavefunction, j where I = r, are the coordinates of all the particles... 

The problem of node locations—the sign problem in quanmm Monte Carlo —remains one of the major obstacles to obtaining exact solutions for systems of more than a few electrons. In analytic variational calculations and in VQMC, the locations of the nodal smfaces of a trial wavefunction may be and usually are optimized along with the rest of the wavefunction in the attempt to reach a minimum in the expectation value of the energy. In DQMC and GF-QMC, the node locations are not so easily varied. 

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