Pu, Han2021-05-032021-05-032021-052021-04-23May 2021Xu, Youjiang. "Designing Quantum Multicritical and Flat-Band Models via Hamiltonian Engineering." (2021) Diss., Rice University. <a href="https://hdl.handle.net/1911/110475">https://hdl.handle.net/1911/110475</a>.https://hdl.handle.net/1911/110475Atomic, molecular, and optical (AMO) systems often feature great controllability. As such, they offer ideal platforms to explore various kinds of quantum phenomena. Designing artificial quantum systems that possess novel and exotic properties is one of the major tasks of theorists working in the AMO field. In this dissertation, we introduce our work on designing novel Hamiltonians which give rise to multicriticality or flat bands. In the first half of the dissertation, we study the multicriticality. Quantum many-body systems that support multicritical quantum phase transitions are quite rare. However, we find that, in an important generalization of the Dicke model, the superradiant quantum phase transitions can become multicritical. For a subclass of experimentally realizable schemes, multicritical conditions of arbitrary order can be expressed analytically in compact forms. As such, experiments can be readily designed to achieve quantum phase transition of desired order. The phase transition happens both in the thermodynamic limit and the classical oscillator limit. We compare the quantum fluctuation in the two cases by calculating the atom-photon entanglement entropy. We find that the order of the criticality strongly affects the critical entanglement entropy. In the second half of the dissertation, we propose a powerful and convenient method to systematically design flat-band lattice models. Flat bands often lead to exotic strongly correlated emergent quantum phenomena. We use this method to generate several classes of lattice models, including models with both short- and long-range hoppings, both ordinary and magnetic translational symmetry, both topologically trivial and non-trivial flat bands.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.MulticriticalFlat-bandThesis2021-05-03