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The last years have witnessed dramatic progress in experimental control and theoretical modeling of quantum simulations based on ultracold atoms. Major recent developments include synthetic gauge fields for neutral atoms, which allow the simulation of topologically nontrivial phases of matter with strong interactions. I will discuss two examples:  We consider a spinful and time-reversal invariant version of the Hofstadter-Harper problem, which has been realized in ultracold atoms, with an additional staggered potential and spin-orbit coupling. Without interactions, the system exhibits various phases such as topological and normal insulator, metal and semi-metal phases with two or even more Dirac cones. Using real-space dynamical mean-field theory (DMFT), we investigate the stability of the Quantum Spin Hall state in the presence of strong interactions. To test the bulk-boundary correspondence between edge mode parity and bulk Chern index of the interacting system, we calculate an effective topological Hamiltonian based on the local self-energy of DMFT.  We furthermore investigate the Haldane honeycomb lattice tight-binding model, for bosons with additional local Hubbard interactions. We analyze the ground state phase diagram at filling one, and uncover three distinct phases: a uniform superfluid (SF), a chiral superfluid (CSF) and a plaquette Mott insulator with local current loops (PMI). 

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Walter Hofstetter, Johann Wolfgang Goethe-Universität Frankfurt
TP seminar room 0.03
Contact: Sebastian Diehl