Variational Monte Carlo Method Combined with Quantum-Number Projection and Multi-Variable Optimization

TL;DR

This paper enhances the variational Monte Carlo method by introducing a highly flexible wave function form with extensive parameters and symmetry projections, significantly improving accuracy for strongly correlated electron systems.

Contribution

It combines a generalized variational wave function with symmetry projection and advanced optimization to achieve higher accuracy in strongly correlated systems.

Findings

Achieved higher accuracy than conventional VMC methods.

Successfully treated long- and short-range correlations.

Implemented using Pfaffians and stochastic reconfiguration.

Abstract

Variational wave functions used in the variational Monte Carlo (VMC) method are extensively improved to overcome the biases coming from the assumed variational form of the wave functions. We construct a highly generalized variational form by introducing a large number of variational parameters to the Gutzwiller-Jastrow factor as well as to the one-body part. Moreover, the projection operator to restore the symmetry of the wave function is introduced. These improvements enable to treat fluctuations with long-ranged as well as short-ranged correlations. A highly generalized wave function is implemented by the Pfaffians introduced by Bouchaud et al., together with the stochastic reconfiguration method introduced by Sorella for the parameter optimization. Our framework offers much higher accuracy for strongly correlated electron systems than the conventional variational Monte Carlo methods.