Advancing many-body methods for electronic structure calculations

Ab initio calculations of materials complement experimental techniques by enabling prediction of properties of materials, as well as accessing quantities that are difficult or impossible to measure in the lab. In strongly correlated materials, properties depend strongly on the coordination of many electrons together, requiring many-body descriptions that explicitly capture electron interactions. This dissertation advances the methods available for ab initio many-body calculations in several areas. In this work, I analyze the capabilities and limitations of a new formula for calculating bulk electric quadrupole moments of many-body wave functions. Interpreting the quadrupole as the result of dipoles flowing through the material highlights subtleties of defining this quantity. With the aim of streamlining development of new formulas and algorithms, I introduce PyQMC, a new implementation of quantum Monte Carlo (QMC) in Python. PyQMC reduces the human time in algorithm development and workflow design through a modular, easy-to-modify codebase. The capabilities of PyQMC are brought to my next project, characterizing spin fluctuations in the ground state of unconventional superconductor CaCuO2. Multi- determinant QMC trial functions are shown to capture spin fluctuations in the undoped parent compound and orbital optimization is demonstrated to be viable on these wave functions, establishing the basis for analyzing spin fluctuations in the less understood doped material. Moving towards excited states, I analyze an algorithm for calculating excited states using many-body wave function based techniques. The approach introduces the first variational principle for an ensemble of trial states, where an objective function is minimized only by the ensemble of the lowest N eigenstates. My work opens the path towards constructing an effective model of the cuprates at QMC level accuracy, which requires high-accuracy ground and excited states and reliable characterization of the spin and charge correlations in the materials. The tools and methods I present will transfer to accurate characterization of other systems and support future efforts to understand and model strongly correlated materials.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Materials Science & Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Wheeler, William A

Contributors dc:contributor

• Wagner, Lucas K
• Schleife, Andre
• Shoemaker, Daniel P
• Perry, Nicola H

• Quantum Monte Carlo
• Many-body Methods
• Many-body Wave Functions
• Electronic Structure
• Excited States

Statement dc:rights

• Copyright 2024 William Wheeler

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/125507

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F125507