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Adam Carl Chiciak, Physics - Final Oral Exam for the Ph.D., Title: Competing and Cooperating Orders in the Three-Band Hubbard Model:
A Comprehensive Quantum Monte Carlo and Generalized Hartree-Fock Study 

https://cwm.zoom.us/j/97356326078?pwd=ZHQ4MTdwcWZyR1lmVm5iYk1rSllSZz09

Zoom password is available upon request. Please email Ellie at evwilk@wm.edu.

Abstract: Significant progress has been made in studying strongly correlated electronic systems with major focus on understanding high-temperature superconductivity. At the center of these studies are the so-called cuprates, which are characterized by a quasi-2D Copper-Oxide plane in which superconductivity is believed to arise. However, despite years of study focused on the one-band Hubbard Hamiltonian, the superconducting order is still unknown. Recent experiments indicate that the oxygen p-bands play a significant role as non-trivial hole carriers, so we find it fit to study the three-band Hubbard (Emery) model, which treats the oxygen p-orbitals explicitly. We perform extensive generalized Hartree-Fock and auxiliary-field quantum Monte Carlo (AFQMC) calculations for the three-band Hubbard (Emery) model in the underdoped regime, in order to study the ground-state properties of Copper-Oxygen planes in the cuprates. Firstly, we focus on the magnetic and charge orders, and present results from generalized Hartree-Fock (GHF) calculations where the ground state exhibits a rich phase diagram with hole doping as the charge transfer energy is varied, including ferromagnetic domain walls embedded in an antiferromagnetic background, spin spirals, and nematic order. Secondly, we use these results to guide and feed into exact methods by employing cutting-edge AFQMC techniques with a self-consistent gauge constraint in auxiliary-field space to control the sign problem, we reach supercells containing ? 500 atoms to capture collective modes in the charge and spin orders and characterize the behavior in the thermodynamic limit. The self-consistency scheme interfacing with generalized Hartree-Fock calculations allows high accuracy in AFQMC to resolve small energy scales, which is crucial for determining the complex candidate orders in such a system. We present results on the charge order, spin order, and localization properties as a function of charge-transfer energy.

Bio: Adam Chiciak was born on January 14, 1992 in Hackensack, New Jersey. In high school, he showed interest in multiple sciences including biology, chemistry, and physics. He enrolled at Villanova University as a chemistry major, but quickly changed to astronomy\& astrophysics before settling as a physics major, with minors in mathematics and business. His academic interest led him to graduate school at William \& Mary in the fall of 2014.

His initial interest in plasma physics led him to Professor Vahala to study nonlinear dynamics in his first year summer. He eventually settled in the Shiwei Zhang's computational condensed matter group, focusing on lattice models for highly correlated systems, specifically high-temperature superconducting systems. He focused on the use of a few numerical techniques: generalized Hartree-Fock and auxiliary field quantum Monte Carlo. Post graduation, he hopes to take his knowledge and interest in machine learning and deep learning and apply to problems in the private sector in the growing field of data science.

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