Description
- Abstract:
- The complicated ways in which electrons interact in many-body systems such as most molecules and materials have long been studied without accounting for the effects of conservation laws. Resolving symmetries associated with these conservation laws can not only provide complementary and clarifying lens on electronic behavior but is also sometimes essential for obtaining correct results. In this thesis, I present studies that perform symmetry resolution in many-body simulations for two different contexts: i) finite temperature electronic structure calculations, and ii) zero temperature entanglement measures. In Part I, I introduce a recursive Auxiliary Field Quantum Monte Carlo (AFQMC) algorithm that can directly simulate systems in the canonical ensemble. We apply the method to the fermion Hubbard model and find improved performance over existing approaches including rapid convergence to ground state expectation values. The effects of excitations above the ground state are quantified using an estimator-agnostic approach including studying the temperature dependence of the purity and overlap fidelity of the canonical and grand canonical density matrices. As an important application, we show that thermometry approaches often exploited in ultra-cold atoms that employ the analysis in the grand canonical ensemble may lead to an under-estimation of extracted temperatures with respect to the Fermi temperature. In Part II, I combine the recursive AFQMC with a modified swap algorithm to measure the accessible entanglement, the entanglement available to a system subject to fixed particle number due to superselection rules, for strongly interacting fermion systems for the first time. The combined algorithm is applied to characterize the phase transitions in the bilayer Hubbard model and the Su–Schrieffer–Heeger-Hubbard model. Here, we utilize these entanglement measures alongside the corresponding particle and spin probability distributions and demonstrate that these quantum informational metrics more clearly resolve around the phase transitions and crossovers than the unresolved entanglement entropy and even certain local order parameters. Overall, this thesis provides new means of characterizing the electronic behavior within quantum systems, potentially deepening our comprehension of the intricate interplay between many-body correlations and conservation laws that underlie quantum phase transitions and crossovers.
- Notes:
- Thesis (Ph. D.)--Brown University, 2023
Citation
Shen, Tong,
"Recursive Auxiliary Field Quantum Monte Carlo: From Simulations in the Canonical Ensemble to Entanglement Measures"
(2023).
Chemistry Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://repository.library.brown.edu/studio/item/bdr:zna5f2mg/
