Quantum Monte Carlo: Advances and Challenges in Strongly Correlated Systems

Speaker:  Dr. Scott Jensen, University of Illinois

Abstract:

Since their development in the 1950s and 60s, Quantum Monte Carlo (QMC) methods have become essential computational tools for exploring strongly correlated systems across nuclear, chemical, and condensed matter physics. Despite substantial progress, major challenges remain in understanding certain paradigmatic systems, motivating ongoing advances in QMC. For instance, predicting high-pressure structures and phase transitions in the hydrogen phase diagram is particularly challenging. In the arguably simpler system of the unitary Fermi gas (UFG), a paradigm model for strongly correlated superfluids, qualitative properties in the so-called “pseudogap regime” remain debated. This regime is characterized by pairing correlations that persist above the superfluid transition temperature.

In this talk, I will discuss recent advances in QMC methods that enable controlled calculations for the UFG. I will then introduce machine-learned interatomic potentials that achieve QMC-level accuracy for dense hydrogen, presenting new findings that support our recent prediction of a high melting line up to 180 GPa. Finally, I will share recent results on the liquid-liquid phase transition (LLPT) in hydrogen and its implications for future theoretical studies.