Wave function optimization in the variational Monte Carlo method

TL;DR

This paper introduces an efficient iterative scheme for wave function optimization in variational Monte Carlo, enabling highly accurate calculations for complex quantum models with multiple parameters.

Contribution

The paper presents a new, rapidly converging optimization method within VMC that improves upon existing stochastic schemes and allows simultaneous optimization of wave function components.

Findings

The new scheme achieves high accuracy in 1D Heisenberg and 2D t-J models.

It converges faster than the standard Newton method.

Simultaneous optimization of Jastrow and determinantal parts is demonstrated.

Abstract

An appropriate iterative scheme for the minimization of the energy, based on the variational Monte Carlo (VMC) technique, is introduced and compared with existing stochastic schemes. We test the various methods for the 1D Heisenberg ring and the 2D t-J model and show that, with the present scheme, very accurate and efficient calculations are possible, even for several variational parameters. Indeed, by using a very efficient statistical evaluation of the first and the second energy derivatives, it is possible to define a very rapidly converging iterative scheme that, within VMC, is much more convenient than the standard Newton method. It is also shown how to optimize simultaneously both the Jastrow and the determinantal part of the wave function.