The project has made substantial progress in the understanding and computational tools available to probe interacting electron systems. As explained above, these are fundamental to being able to simulate the physics of molecular reactions, materials and on to more exotic forms of quantum matter. We have made substantial progress along a number of complementary and intertwined directions. One main achievement has been the formulation of a rigorous ‘embedding’ formulation. Calculating the exact ground state of a quantum many-body system is formally exponentially difficult with system size, and so one approach it to try to split this problem into multiple smaller ones which can be solved. This exposed fundamental questions about how to split apart a quantum system of many electrons, but pulling on this thread led to a number of important developments and practical formulations of embedding theories that have grown into important computational tools. We have applied these approaches to understand realistic materials in the ‘thermodynamic limit’, i.e. the large system size, and in an important publication have shown these results to be well within the scatter due to the uncertainty of existing state-of-the-art approximations. Importantly, one of the main outcomes of this work has been the public availability of efficient and well-maintained software packages which implement the developed algorithms for electronic structure. Our package ‘vayesta’ that implements these embedding approximations is now being used by a number of independent groups and governmental agencies, currently being applied to understand next-generation battery materials (as one example). Several publications have detailed the development of this quantum embedding thrust. Recently, we generalized some of the questions that arise in quantum embedding, to ask the question of the ‘optimal’ choice of how quantum particles in a subsystem should interact with each other to mimic the effect of the rest of the neglected system. This question led to the formulation of an effective interaction, which we dubbed the `moment-constrained random phase approximation’, which was recently published. An independent study has built on this work, comparing it to existing approaches, and found it to be the optimal choice for designing effective interactions.
Being able to simulate the interactions of many electrons in different systems is important, but we also considered the ability to control these systems in this project. For this, we have to consider the time-dependence of the electronic structure under the action of some driving perturbation (e.g. laser field). For this, we developed and applied modifications to our stochastic quantum Monte Carlo methods to simulate the properties as they evolved in time. In particular, we considered the phenomena of ‘high-harmonic generation’, where coherent light sources on the shortest timescales accessible are generated by ionizing systems and then recombining the electrons at high speed. However, this new phenomena had only been simulated in isolated atomic systems, and almost no investigations had been performed on solid state materials, especially with strong correlation effects. We simulated these effects in two-dimensional Mott insulators for the first time, finding important dynamical phase transitions, where the laser can melt the quantum order established in the equilibrium electronic structure.
Beyond this, with collaborators at Tulane university, we extended this to the idea of ‘tracking control’ theory. We derived a time-dependent perturbation which ensured that a particular expectation value of a material followed a desired trajectory in time. In this way, we could design the response of a material to laser light in order to follow some pre-determined trajectory. This novel approach for the quantum control of materials captured the attention of wider popular media, and was the subject of a significant number of articles in science magazines, including ‘Physics World’ and ‘Nature Materials’.
