Ab Initio Simulations of Light Nuclear Systems Using Eigenvector Continuation and Auxiliary Field Monte Carlo

Abstract

In this work, we discuss a new method for calculation of extremal eigenvectors and eigenvalues in systems or regions of parameter space where direct calculation is problematic. This technique relies on the analytic continuation of the power series expansion for the eigenvector around a point in the complex plane. We start this document by introducing the background material relevant to understand the basics of quantum mechanics and quantum field theories on the lattice, how we perform our numerical simulations, and how this relates to the nuclear physics we probe. We then move to the mathematical formalism of the eigenvector continuation, which is rooted in analytic function theory and linear algebra. We then discuss how these techniques are implemented numerically, with a discussion about the computational costs. Finally, we discuss applications of this method to full, quantum many-body systems. These include neutron matter, the Bose-Hubbard model, the Lipkin model, and the Coulomb interaction in light nuclei with LO chiral forces. These systems cover two categories of interest to the field: systems with a substantial sign problem, or systems that exhibit quantum phase transitions.

arXiv commentPh.D. Dissertation. Submitted to Michigan State University. Supervised by Dean J. Lee. 118 pages, 63 figures

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Cited by in corpus (6)

• Efficient emulators for scattering using eigenvector continuation
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• Fast emulation of quantum three-body scattering
• Fast & rigorous predictions for $A=6$ nuclei with Bayesian posterior sampling
• Self-learning Emulators and Eigenvector Continuation
• Chiral Effective Field Theory after Thirty Years: Nuclear Lattice Simulations