Browsing by Author "Hazzard, Kaden"
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Item Electron correlation in extended systems via quantum embedding(2015-06-17) Bulik, Ireneusz W; Scuseria, Gustavo E.; Kolomeisky, Anatoly B; Hazzard, KadenThe 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.Item Exact and rigorous methods in quantum many body physics(2022-08-10) Wang, Zhiyuan; Hazzard, KadenQuantum 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.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, KadenSynthetic 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.