## Current Research

### Pairing functions in Continuum Quantum Monte-Carlo

Continuum Quantum Monte-Carlo (QMC) identifies a class of numerical methods that allow high accuracy computation of the electronic properties of materials and model systems.

In particular, Diffusion Monte-Carlo (DMC) has been used to successfully describe many real systems such as molecules, clusters and periodic solids. The most important limitation on DMC accuracy is the so-called "fixed node" error. Reaching beyond this limit has proven extremely challenging.

Fixed node error can be alleviated by replacing the Slater-Jastrow trial wavefunction traditionally used to initialise a Diffusion Monte-Carlo calculation by a wavefunction whose nodal surface more closely resembles the true ground state wavefunction.

Several such wavefunctions have been proposed. In this project, we investigate pairing wavefunctions. These wavefunctions 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 investigate how well pairing functions behave in larger systems, looking in particular at size extensivity.

I am working on integrating these pairing wavefunctions in the widely used QMC code Casino.

This research is conducted under Richard Needs' supervision, with the help of Pablo López Ríos.

### Ultracold atomic gases

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.

Recently, experimentalists have shown that they could trap and control a small number of atoms in a harmonic trap with single atom accuracy. In this project, we use exact diagonalisation and Quantum Monte-Carlo methods to describe how the experimental setup can be used to probe previously unobserved quantum phenomena such as itinerant ferromagnetism and FFLO phases in superconductors.

This research is conducted with Gareth Conduit.