289 research outputs found

    Mott Insulator-Superfluid Transition in a Generalized Bose-Hubbard Model with Topologically Non-trivial Flat-Band

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    In this paper, we studied a generalized Bose-Hubbard model on a checkerboard lattice with topologically nontrivial flat-band. We used mean-field method to decouple the model Hamiltonian and obtained phase diagram by Landau theory of second-order phase transition. We further calculate the energy gap and the dispersion of quasi-particle or quasi-hole in Mott insulator state and found that in strong interaction limit the quasi-particles or the quasi-holes also have flat bands.Comment: 13 figures, 9 page

    Translation invariant topological superconductors on lattice

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    In this paper we introduce four Z_2 topological indices zeta_k=0,1 at k=(0,0), (0,pi), (pi, 0), (pi, pi) characterizing 16 universal classes of 2D superconducting states that have translation symmetry but may break any other symmetries. The 16 classes of superconducting states are distinguished by their even/odd numbers of fermions on even-by-even, even-by-odd, odd-by-even, and odd-by-odd lattices. As a result, the 16 classes topological superconducting states exist even for interacting systems. For non-interacting systems, we find that zeta_k is the number of electrons on k=(0,0), (0,pi), (pi, 0), or (pi,pi) orbitals (mod 2) in the ground state. For 3D superconducting states with only translation symmetry, there are 256 different types of topological superconductors.Comment: 4 pages, RevTeX

    Topological Interplay between Knots and Entangled Vortex-Membranes

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    In this paper, the Kelvin wave and knot dynamics are studied on three dimensional smoothly deformed entangled vortex-membranes in five dimensional space. Owing to the existence of local Lorentz invariance and diffeomorphism invariance, in continuum limit gravity becomes an emergent phenomenon on 3 + 1 dimensional zero-lattice (a lattice of projected zeroes): on the one hand, the deformed zero-lattice can be denoted by curved space-time for knots; on the other hand, the knots as topological defect of 3 + 1 dimensional zero-lattice indicates matter may curve space-time. This work would help researchers to understand the mystery in gravity
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