Almost all the properties of solids – their chemistry, electrical conductivity, strength, hardness, ductility, melting point, dielectric constant, refractive index, magnetic moment, and so on – depend on quantum mechanics. One can measure the density of a brick without using quantum theory, but why does a brick have the density it does? The density depends on the sizes of the atoms, and the sizes of the atoms depend on the sizes of the electron orbits around those atoms. The orbits can only be described using quantum mechanical wave functions satisfying the Schrödinger equation. Most questions about molecules and solids work like this: as soon as you say "why" more than once or twice, you find yourself face-to-face with quantum theory.

The Schrödinger equation can only be solved by hand in the very simplest systems, so most of my work on the quantum theory of solids is highly computational. The technique with which I am most closely associated is the quantum Monte Carlo method, in which massively parallel computers are used to carry out huge numbers of idealised "experiments", averages of the results of which yields the results of real experiments almost exactly. In large systems, in particular, quantum Monte Carlo methods are far more accurate than any other available approach. My group was among the first to apply quantum Monte Carlo techniques to real solids and remains one of the leading groups in the field. The main drawback of quantum Monte Carlo simulations is that they are very hard to do and the range of tractable physical problems is correspondingly small. Since I am interested in physics as well as computational methods, I also use simpler approaches such as density functional theory when appropriate.

My current work, much of which is done in collaboration with James Spencer and David Pfau from Google Deepmind, combines the use of neural networks with quantum Monte Carlo methods. The many-electron wave function is represented as a neural network that takes the electron positions and spins as inputs and produces the corresponding value of the wave function as an output. The weights and biases of the neural network wave function can be learnt using the variational principle alone, without the use of external data, and the results obtained after the variational optimization are remarkably accurate. Recent projects have used neural wave functions to investigate the crystallization of a uniform electron gas as the density is reduced, positron binding to molecules, and superfluidity. During the last few years, I have also become interested in extending the quantum mechanical approaches used to study solids beyond the Born-Oppenheimer approximation, taking proper account of the exchange of energy between spins, electrons, and ions. Another recent interest has been the physics of warm dense matter. Seen from the point of view of a condensed matter physicist, warm dense matter is a misnomer: it is enormously hot - the thermal energy is comparable to the Fermi energy - but not particularly dense.

When not researching or answering email, most of my working life is spent teaching. I am currently lecturing second-year undergraduate courses on quantum physics and electromagnetism.