Pairing wave functions for quantum Monte Carlo

Pascal Bugnion, Pablo López Ríos, Richard Needs

Diffusion Monte-Carlo (DMC) has been used to describe many real and model systems, usually displaying impressive agreement with experiments while maintaining favourable scaling with system size.

The accuracy of diffusion Monte-Carlo is ultimately limited by the so-called ‘fixed-node’ error, which depends on the quality of the trial wave function used as input to the algorithm.

Typically, the DMC trial wave function is generated in a variational quantum Monte Carlo (VMC) calculation, where it is optimized to minimize the VMC energy. It is heuristically believed that trial wave functions with lower VMC energies will have better nodal surfaces.

To reduce fixed-node error, we therefore need VMC trial wave functions whose functional form is close to the ground state wave function. In this project, we will study a class of such wave functions: pairing wave functions. Pairing wave functions contain parameters which can be optimized variationally, allowing in principle the determination of a better nodal surface. This produces lower DMC energies and more accurate results. We shall investigate how well pairing functions behave in larger systems, looking in particular at size extensivity.

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