UC Irvine

Warm Dense Matter (WDM) can be found in a myriad of useful and worthwhile applications, whether it be in the ongoing study of inertial confinement fusion, novel shock experiments, or planetary interiors. One crucial tool that has revolutionized our understanding of WDM over the last few decades has been Finite-Temperature Density Functional Theory (FT-DFT), which has enabled various groundbreaking simulations in the field (often when experimental studies were too difficult and costly to be performed). Although successful, modern implementations of FT-DFT suffer from significant drawbacks, namely the large computational burden inherent to studying high-temperature materials, and the lack of sophisticated approximations describing temperature-dependent exchange-correlation interactions. The research contained in this dissertation works to address these fundamental challenges both directly and indirectly.

Chapter 2 serves as an introduction to the underlying theorems of ground-state DFT, all of which extend to nonzero temperatures, and are depicted through illustrative examples using the Hubbard dimer. Chapter 3 introduces Density-Corrected DFT, a novel theory studying the origin of errors in functional approximations, and a means of analysis for approximations in both the ground state and at finite temperatures.

Chapter 4 derives exact conditions for Ensemble Density Functional Theory, all of which provide insight into the behavior of temperature-dependent exact conditions for FT-DFT. Chapter 5 proposes a novel temperature-dependent generalized gradient approximation, the locally thermal Perdew–Burke–Ernzerhof (ltPBE) approximation, for FT-DFT calculations of WDM. This temperature-dependent approximation is the first of its kind, with its origin rooted entirely in a model of the PBE gradient-dependent exchange-correlation hole density at nonzero temperatures.

Lastly, Chapter 6 discusses how Tensor Processing Units (hardware that was originally designed to perform machine-learning tasks) has been repurposed to perform highly efficient Kohn-Sham DFT calculations. This in particular has significant impact on future studies of WDM, where high temperatures greatly increase the computational cost of calculations.