# Professor Matthew Foulkes

**Department:** Physics**Institution:** Imperial College London**Email:** wmc.foulkes@imperial.ac.uk**Phone:** +44 (0)20 7594 7607**Website**: https://www.imperial.ac.uk/people/wmc.foulkes

## Research summary

Chemical bonds in solids are built using electrons, which are highly quantum mechanical and act more like waves than particles. Understanding and simulating bonding in solids requires the use of quantum theory. In principle, the QM properties of many-electron systems can be found by solving the many-electron Schrodinger equation, but in practice this is possible only for atoms and small molecules. In solids, the best one can do is adopt a statistical approach such as quantum Monte Carlo (QMC). Using large parallel computers, it is now possible to simulate systems of a few thousand interacting electrons, which is enough to calculate the properties of real solids with remarkable accuracy. Accurate though QMC may be, many properties of materials involve groups of atoms too large to be tackled that way. In such cases, or when high accuracy is unnecessary, we also use density-functional theory and tight-binding methods, which are less accurate but more flexible. Recent work has included: studies of the metal-insulator transition in hydrogen at high pressure; a mathematical derivation of the most general Hubbard-like Hamiltonian allowed by symmetry; the development of the density matrix quantum Monte Carlo (QMC) method for simulating systems of interacting electrons at high temperature; the use of density matrix QMC to construct the first accurate local density approximation for the warm dense electron gas; and density-functional-based studies of grain boundaries in alumina. Current projects include an investigation of the use of capacitors for energy storage and an attempt to find ways of simulating and understanding the spin-orbit-induced coupling between magnetic moments and atomic positions that leads to the Einstein–de Haas effect.

## Keywords

Fusion Materials, Nuclear Materials, Alumina, Magnetic Materials, Transition Metals, Channelling, Defects In Solids, Grain Boundaries, Heat Conduction, High Pressure, Non-Adiabatic Processes, Planetary Interiors, Planetary Materials, Point Defects, Extreme Conditions, Radiation Damage, Correlated Electron-Ion Dyn, CASINO, Exchange-Correlation Func, Massively Parallel Computing, Monte Carlo Techniques, Quantum Monte Carlo, TDDFT, Tight-Binding Methods, Radiation Damage