Pascal Bugnion, Gareth Conduit, Richard Needs

Ultracold atomic gases provide a test bed for the study of fundamental quantum condensed matter phenomena. We are particularly interested in fermionic cold atom gases as these can be used to model collective electronic processes in the solid state.

The dynamics of a dilute ultracold atomic gas is dominated by short-range interactions between the atoms, typically characterized by the scattering length of the inter-particle potential. Modelling this regime is challenging for QMC methods as the wave function diverges when particles coalesce.

Previous attempts at circumventing this divergence have normally involved using an effective potential to model the inter-particle interactions. This effective potential is constructed to reproduce some of the features of the true potential while avoiding its pathological behaviour. We investigate the applicability of the wide range of methods developed by the electronic structure and chemistry community to the development of an effective potential for interactions between cold atoms.

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.