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Low-dimensional quantum systems from novel constituents Li, Chengshu


Recent decades have seen a proliferation of unconventional quasiparticles in condensed matter systems. Majorana fermions, theoretically predicted in several setups and of great interest in topological quantum computation, are a focus of intense research efforts. Higher-spin moments, relevant for both solid-state compounds and cold atoms, are of great theoretical interest as they interpolate between the quantum and classical limits but sometimes show surprising behavior. In the meantime, successful fabrication and characterization of low-dimensional systems have brought new phenomenology and physical insights. In this dissertation I will theoretically explore a few low-dimensional models using Majorana fermions and higher-spin moments as building blocks. I will first discuss a generalized family of the celebrated Sachdev-Ye-Kitaev model, a zero-dimensional all-to-all Majorana model that exhibits non-Fermi liquid behavior and is holographically dual to a black hole. The generalized model has a phase transition between a non-Fermi liquid and a disordered Fermi liquid. Then I will discuss the Heisenberg model with higher spins, with a focus on chaos and information scrambling. Using matrix-product-state-based methods, we are able to obtain numerical results for spin up to 4 and characterize the Lyapunov growth. After that I will discuss a generalization of the Hubbard model to Majorana fermions on the honeycomb lattice. Unlike previous similar models, we find topological phases with (anti-)chiral edge modes for weak interaction. Finally I will show a construction of explicit supersymmetric Majorana model on the kagome lattice, where a family of exact solutions is found and the nature of supersymmetry breaking is explored.

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