Chen, Yushao2024-09-162024-09-162024-09-162024-09-12https://hdl.handle.net/10012/21001This thesis explores quasi one-dimensional (quasi-1D) quantum spin systems, specifically focusing on Kitaev ladders, Heisenberg ladders, and Motzkin chains. The research employs a combination of analytical and numerical tools to systematically study the phase diagrams of these low-dimensional spin lattices, developing a standardized pipeline for analyzing future models of interest within the field of quantum physics. At the core of this investigation is the deep interconnection between low-dimensional quantum systems and their corresponding tensor network structures. Utilizing Matrix Product States (MPS) and the Density Matrix Renormalization Group (DMRG) methodologies, the thesis provides detailed insights into the phase behaviors of these quasi-1D systems. This includes examining novel phenomena such as quantum spin liquids, various magnetic orderings, and symmetry-protected topological orders. These findings not only enhance our understanding of quantum physics but also highlight the effectiveness and adaptability of tensor network approaches in tackling complex theoretical problems.enQuantum Many-Body SystemsTensor NetworksKitaev ModelsHeisenberg LaddersMotzkin ChainsLuttinger LiquidQuantum Phase TransitionsDensity Matrix Renormalization GroupDoctoral Thesis