UNC-CH Physics and Astronomy PhD Defense

Andrew Loheac

“Computational techniques to address the sign problem in non-relativistic quantum thermodynamics”

Understanding quantum many-body physics is crucial to physical systems throughout condensed matter, high-energy, and nuclear physics, as well as the development of new applications based on such systems. Stochastic techniques are generally required to study strongly-interacting quantum matter, but are frequently hindered by the sign problem, a signal-to-noise issue which breaks down importance sampling methods for many physical models. In this talk, I will discuss several novel stochastic nonperturbative and semi-analytic perturbative techniques to circumvent the sign problem in the context of non-relativistic quantum gases at finite temperature. These techniques include an extension to hybrid Monte Carlo based on an analytic continuation, complex Langevin, and an automated perturbative expansion of the partition function, all of which use auxiliary field methods. First predictions for thermodynamic equations of state of non-relativistic Fermi gases in spin-balanced and spin-polarized systems will be presented, including calculations of the density, magnetization and pressure equations of state. These calculations are benchmarked in one spatial dimension and extended to two and three dimensions, including a study of the unitary Fermi gas. The application of convolutional neural networks to improve the efficiency of Monte Carlo methods will also be discussed.