We propose a generalized Dicke model which supports a quantum tricritical point. We map out the phase diagram and investigate the critical behaviors of the model through exact low-energy effective Hamiltonian in the thermodynamic limit. As predicted by the Landau theory of phase transition, the order parameter shows non-universality at the tricritical point. Nevertheless, as a result of the separation of the classical and the quantum degrees of freedom, we find a universal relation between the excitation gap and the entanglement entropy for the entire critical line including the tricritical point. Here the universality is carried by the emergent quantum modes, whereas the order parameter is determined classically.
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 2D 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 px + ipy 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.
We consider an important generalization of the Dicke model in which multi-level atoms, instead of two-level atoms as in conventional Dicke model, interact with a single photonic mode. We explore the phase diagram of a broad class of atom-photon coupling schemes and show that, under this generalization, the Dicke model can become multicritical. For a subclass of experimentally realizable schemes, multicritical conditions of arbitrary order can be expressed analytically in compact forms. We also calculate the atom-photon entanglement entropy for both critical and non-critical cases. We find that the order of the criticality strongly affects the critical entanglement entropy: higher order yields stronger entanglement. Our work provides deep insight into quantum phase transitions and multicriticality.
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