Predicting the Extreme

Introduction

Matter at extreme densities and temperatures is ubiquitous in nature and occurs, e.g., in planetary interiors. In addition, such warm dense matter (WDM) conditions are of high importance to technological applications such as nuclear fusion. Therefore, there has been a remarkable investment in the experimental realization of WDM in large research facilities around the globe, leading to a number of spectacular discoveries.

Theoretical Challenges

Yet, the absence of a reliable theoretical description of WDM is severely hampering this progress. This is best illustrated by considering hydrogen, the most simple and abundant element in the universe. Even here, a multitude of pressing questions continues to be unanswered:

1. What is the nature of the insulator-to-metal phase transition of hydrogen at high pressure?
2. How do electronic properties of hydrogen impact the evolution of giant planets and brown dwarfs?
3. How can a hydrogen pellet best be compressed to efficiently produce electrical power in a fusion reactor?

Computational Bottlenecks

The central obstacle on the path towards answers to these questions is the fermion sign problem, one of the most fundamental computational bottlenecks in physics, chemistry, and related disciplines. Recently, a number of methodological breakthroughs have allowed me to present the first accurate data for the electronic properties of WDM over substantial parts of the relevant parameter space. This was achieved using supercomputers and the data-driven construction of AI surrogate models.

Proposed Solution

In PREXTREME, I propose to explore a hitherto unattempted complete solution to the sign problem, which will allow me to answer many questions about warm dense hydrogen and heavier elements with a direct impact on applications in material science, astrophysical models, and nuclear fusion.

Broader Implications

Moreover, my envisioned approach will revolutionize quantum many-body theory, with important implications for a gamut of fields including high-temperature superconductivity, high-pressure physics, and ultracold atoms.