Browsing by Author "Hazzard, Kaden"

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Electron correlation in extended systems via quantum embedding
    (2015-06-17) Bulik, Ireneusz W; Scuseria, Gustavo E.; Kolomeisky, Anatoly B; Hazzard, Kaden
    The pursuit of accurate and computationally efficient many-body tools capable of describing electron correlation is a major effort of the quantum chemistry community. The accuracy of chemical predictions strongly depends on the ability of the models to account for electron correlation. As the computational demand scales unfavourably with the size of the system, an efficient way of identifying relevant degrees of freedom may be an interesting avenue. In this thesis, a quantum embedding approach is employed to study lattice systems, polymers, and crystals. Numerical data shows the accuracy of the quantum embedding theory when combined with high-level many-body techniques. As the size of the units that are embedded grows, a more approximate and more computationally affordable tools are called for. In this thesis, we investigate the possibility of forming such methods in the framework of coupled cluster theory. We believe that the tools presented in this thesis could be important for accurate treatment of electron correlation in applications to realistic materials.
  • Thumbnail Image
    Item
    Exact and rigorous methods in quantum many body physics
    (2022-08-10) Wang, Zhiyuan; Hazzard, Kaden
    Quantum many body physics is an exciting research area, involving novel phases of matter with fundamentally new properties, but is also notoriously hard due to complexity of interacting quantum systems. Some popular approaches involve approximation techniques and numerical simulations, which are known to fail in several important cases. In contrast, rigorous mathematical tools, such as exact solutions and operator inequalities, have a narrower range of applicability, but provide guaranteed results and insights into the underlying physical mechanisms. This research aims to develop new techniques in this direction and use them to explore novel phases of matter. My first direction is to construct toy models where exact solutions are possible. Such models are important as they prove that certain physical phenomena are theoretically possible in nature, and often lead to the discovery of new phases. Such insights are provided by three exactly solvable models I have discovered: (1) a family of 1D quantum spin models hosting free parastatistical quasiparticles (an exotic type of identical particles beyond fermions, bosons, and anyons), proving for the first time that parastatistics is theoretically possible as an emergent phenomenon; (2) a 3D classical Ising model whose phases are characterized by topological features of certain loop observables, suggesting existence of previously unknown classical phases and phase transitions with topological order parameters; and (3) a family of models with exact p-wave superconducting ground states demonstrating the existence of Majorana quasiparticles and non-Abelian statistics in particle number-conserving systems. My second direction is to derive rigorous bounds and exact constraints on physical observables, which are applicable to large families of quantum many-body systems. I present three directions of progress: (1) a method that dramatically improves the upper bounds on the speed of information propagation in locally-interacting systems, which significantly extends the scope of these bounds and enables new applications; (2) bounds on finite-size errors in numerical simulations of lattice systems, including quench dynamics and gapped ground states; and (3) a locality bound on gapped ground states of power-law interacting systems, which leads to a generalization of the aforementioned error bounds to such systems. These error bounds have important theoretical implications such as proving the existence of the thermodynamic limit and stability of phases, and are practically useful in determining the validity of finite-size numerical simulations.
  • Thumbnail Image
    Item
    Exploring the structure-function relationship of biomacromolecules: simulation and prediction of structural behavior of viral proteins and chromatin
    (2024-07-01) Dodero Rojas, Esteban; Onuchic, José Nelson; Hazzard, Kaden; Kolomeisky, Anatoly
    Biomacromolecules are the main functional constituents in living systems. They exhibit a great diversity of tasks depending on the composition of their monomers. Most protein and chromatin functions emerge from the interactions with other biomacromolecules. This dissertation focuses on viral proteins and chromatin systems, describing the relationship between their structure, composition and function using computational and theoretical models. Chapter 1 presents the motivation and describes the two main studied systems: the SARS-CoV-2 Spike protein and the eukaryote interphase genome. Chapter 2 focuses on the implementation of Structure Based Models to simulate the conformational change of the S2 subunit of the SARS-CoV-2 Spike protein associated with the membrane fusion process. We determined the transition states of the Spike protein, and predicted relevant intermediate states readily available to serve as druggable or vaccine targets. The simulated transitions highlight the role of post-translational modification (branched glycans) during viral entry. This model was further expanded to explore how the neutralizing CV3-25 antibody blocks viral entry by inhibiting the full transition of the Spike protein. Chapter 3 describes a pipeline to infer the efficiency of SARS-CoV-2 epitopes in scaffold vaccine strategies. Using explicit solvent simulations, we observed the dynamics of the target epitopes on exposed environments, similar to their context in scaffold-driven vaccines. When compared with experiments, we noticed that the most experimentally efficient epitope (S1Ep4) correlates with high thermal stability around the Wuhan-1 Spike protein conformation. To assess whether the S1Ep4 epitope would trigger immune response for SARS-CoV-2 variants, we performed explicit solvent simulations of the variant local environment of the epitope. The target epitope showed high conformational stability for all the variants around the Wuhan-1 strain structure. We determined that there is high likelihood the S1Ep4 epitope to incite immunoreponse on all the SARS-CoV-2 variants. Lastly, using the aforementioned simulated transitions of Spike during the membrane fusion, we identify new epitopes in the S2 subunit and the conformational study pipeline was implemented. Two new epitopes on the S2 subunit were proposed in highly conserved regions of the Spike protein, stepping towards pan-coronavirus vaccine strategies. Chapter 4 delves into the correlation between the biochemical composition of the DNA and its structural behavior. We expanded upon previous models to predict the subcompartment annotations of the chromatin based on biomarker enrichment along the genomes; including Histone Modification frequencies, transcriptor factor binding profiles and transcription activities. The prediction method, called PyMEGABASE (PYMB), is based on a graph model with a trainable Potts model. Within the model one node corresponds to the locus subcompartment and the remaining nodes are associated with the biomarker enrichment profiles. Using PYMB, we inferred the subcompartment annotations for hundreds of cell lines in multiple eukaryotes, which allow us to determine the cell identity from the subcompartment profile. In Chapter 5 we aim to increase the accuracy at predicting subcompartments by training a transformer architecture, called TECSAS. The new model is able to outperform PYMB's accuracy by more than 20%. From the new predictions, we determined that the transition region in sequence between subcompartments is approximately 150kbp. Finally, we expanded the model to predict the likelihood of genome loci to bind to nuclear bodies (Lamina, Nucleoli, and Speckles). We demonstrated based on the projection of the predicted likelihoods upon 3D chromatin data on the cell IMR-90 that both Lamina and Speckles create a stronger structural bias than the nucleoli. In summary, we explored the relationship between structure and function in the Spike protein's refolding pathway and demonstrated the significance of the conformational stability of epitopes around the target protein structure for vaccine efficiency. Further, the biochemical composition to structural behavior was examined for chromatin systems by the prediction of subcompartments from biochemical data, as well as the impact of the nuclear bodies, such as the lamina, in the overall ensemble behavior of chromatin systems. Overall, we determined that the mechanisms driving function of biomacromolecules are tightly correlated with their composition and structure.
  • Thumbnail Image
    Item
    Phases in Ultracold Interacting Rydberg Atom Systems With The Su-Schrieffer-Heeger Model Engineered On A Synthetic Dimension
    (Rice University, 2023) Dyall, Charles; Hazzard, Kaden
    Synthetic dimensions encoded into atomic states have emerged as a powerful tool for engineering new phases of matter. These synthetic dimensions are helpful in accessing confgurations that are difcult or impossible to simulate using real space alone. Using Rydberg states to encode these synthetic dimensions allows a high level of control over system parameters. Here we use a mean-feld theory approach to investigate phases of matter that occur in Rydberg atoms with attractive interaction in real space with the synthetic dimension encoded such that it emulates a Su-Schriefer-Heeger (SSH) model lattice. We fnd that this model displays both two and three-site quantum strings in the ground state that demonstrate substantial crossover with larger strings and two-site string phases, respectively.