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 upon 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. This dissertation develops 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. Each technique is used to compute first predictions for thermodynamic equations of state for non-relativistic Fermi gases in spin-balanced and spin-polarized systems for both attractive and repulsive interactions. These results are frequently compared against second- and third-order virial expansions in appropriate limits. The calculation of observables including the density, magnetization, pressure, compressibility, and Tan’s contact 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 is also discussed.Doctor of Philosoph