Browsing by Author "Xu, Youjiang"

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    Building flat-band lattice models from Gram matrices
    (American Physical Society, 2020) Xu, Youjiang; Pu, Han; Rice Center for Quantum Materials
    We propose a powerful and convenient method to systematically design flat-band lattice models, which overcomes the difficulties underlying the previous method. Especially, our method requires no elaborate calculations, applies to arbitrary spatial dimensions, and guarantees to result in a completely flat ground band. We use this method to generate several classes of lattice models, including models with both short- and long-range hoppings, both topologically trivial and nontrivial flat bands. Some of these models were previously known. Our method, however, provides important insight. For example, we have reproduced and generalized the Kapit-Mueller model [Kapit and Mueller, Phys. Rev. Lett. 105, 215303 (2010)] and demonstrated a universal scaling rule between the flat-band degeneracy and the magnetic flux that was not noticed in previous studies. We show that the flat band of this model results from the (over-)completeness properties of coherent states.
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    Designing Quantum Multicritical and Flat-Band Models via Hamiltonian Engineering
    (2021-04-23) Xu, Youjiang; Pu, Han
    Atomic, 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.
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    Number-conserving interacting fermion models with exact topological superconducting ground states
    (American Physical Society, 2017) Wang, Zhiyuan; Xu, Youjiang; Pu, Han; Hazzard, Kaden R.A.
    We present a method to construct number-conserving Hamiltonians whose ground states exactly reproduce an arbitrarily chosen BCS-type mean-field state. Such parent Hamiltonians can be constructed not only for the usual s -wave BCS state, but also for more exotic states of this form, including the ground states of Kitaev wires and two-dimensional topological superconductors. This method leads to infinite families of locally interacting fermion models with exact topological superconducting ground states. After explaining the general technique, we apply this method to construct two specific classes of models. The first one is a one-dimensional double wire lattice model with Majorana-like degenerate ground states. The second one is a two-dimensional p x + i p y superconducting model, where we also obtain analytic expressions for topologically degenerate ground states in the presence of vortices. Our models may provide a deeper conceptual understanding of how Majorana zero modes could emerge in condensed matter systems, as well as inspire novel routes to realize them in experiment.