Artificial Gauge Fields versus Interaction Effects

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The quest of topological phases has been a great challenge the last decades with the realization of quantum Hall effects, Haldane model and quantum spin Hall effect leading more generally to topological insulators, topological superconductors and magnetic systems with Majorana fermions. In this project, the primary goal is to find and characterize new topological phases in the presence of interactions and to suggest real applications in ultra-cold atoms through the implementation of artificial gauge fields in optical lattices. We will study fermions and bosons from the weakly-interacting regime to the strongly-correlated one, then leading to Mott physics with interesting magnetic properties and to fractional quantum Hall phases. We introduce two new platforms in relation with topological proximity effects in novel interfaces and hybrid systems. The project for the second period is organized in four classes, demonstrating our collaborations within this Research Unit: ladders and wire topological models, interacting topological phases and topological proximity effects in quasi-two-dimensional systems, topological characterization and new probes, time-dependent phenomena and light-matter coupling. Regarding the methodology, an effort will be done on quantum field theory techniques and stochastic approaches complemented by some numerical approaches. To tackle properties of timedependent Hamiltonians in the presence of interactions, stochastic approaches and semi-classical analysis will be compared with numerical diagonalizations and effective Floquet theories.