Periodic Reporting for period 4 - WFNQMC (Development of a Novel Computational Toolbox for Stochastic Electronic Structure in Chemistry and Condensed Matter)
Periodo di rendicontazione: 2022-08-01 al 2023-09-30
The interactions between electrons and nuclei provide the glue that binds together all materials and chemicals. The specifics of these interactions give rise to the vast array of different properties around us, ranging from metallic behaviour, to catalytic biomolecules or magnetic interactions. However, while it is now common to design large-scale engineering projects from buildings to planes with accurate computational simulation, it is curious that the techniques for microscopic simulations of the interactions of these most fundamental particles is still very much lacking. An understanding and computational description of these materials and their emergent properties may enable us to design materials with improved properties, or even for example unlock the mechanisms behind some of the most important biological enzymes that enable life?
The aim of this project is to make a leap in our ability to computationally model the nature of interacting electrons, and therefore our ability to predict the emergent properties of the system, without prior information from experiment, allowing us to guide and inform them.The other overarching aim is to bring together the domains of condensed matter theory (dealing with extended, bulk systems), and quantum chemistry (dealing with the electronic interactions in molecules) under a common framework. To do this, we will develop a toolbox of methods, exploiting stochastic (random) sampling of this wavefunction, as well as its combination with other tools at our disposal, including perturbation theory, local embedding, and entanglement structure, in order to advance the algorithms and computational methods which we can use to understand the materials and molecules of fundamental importance in the world around us all.
The aim of this project is to make a leap in our ability to computationally model the nature of interacting electrons, and therefore our ability to predict the emergent properties of the system, without prior information from experiment, allowing us to guide and inform them.The other overarching aim is to bring together the domains of condensed matter theory (dealing with extended, bulk systems), and quantum chemistry (dealing with the electronic interactions in molecules) under a common framework. To do this, we will develop a toolbox of methods, exploiting stochastic (random) sampling of this wavefunction, as well as its combination with other tools at our disposal, including perturbation theory, local embedding, and entanglement structure, in order to advance the algorithms and computational methods which we can use to understand the materials and molecules of fundamental importance in the world around us all.
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’.
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’.
With the project having finished, we can reflect on the number of ways in which the research has enabled a pushing of the state of the art across a number of different techniques and methods in the field, and the insights across different physical systems that this has provided. Within quantum embedding techniques, we have enabled large, correlated materials simulations with unprecedented accuracy, and without any empirical approximations, enabling systematic improvability. This has allowed a new level of insights into correlated solids, including applications to Nickel Oxide, Lanthanum titanate, plasmons in graphene and beyond. Advances in Green’s function methodology for computing bandgaps and charged excitation energies of molecules and materials have enabled conceptual reformulations of existing methods, with improved numerical robustness and reduced technical parameters. These have been made available in professional-quality software packages for all to use freely. We have provided the first computational insights into two-dimensional correlated materials undergoing high-harmonic generation, enabled by the development of advanced stochastic methods beyond the state-of-the-art, to reach the required system sizes necessary to see the emergent physics. These results show a small cross-section of the successes of the project, which have materially moved the dial in terms of the efficiency and reliability of computational simulation for realistic correlated many-electron problems.