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The quest for understanding and exploiting many-body phenomena has received new spur in the last decades by the increasing capacity of harnessing quantum particles to tailor more and more sophisticated systems. Among others, cold atomic gases are one of the most flexible platforms for realising such “Synthetic Quantum Matter”. Here, I focus on the interplay of geometrical constraints, tunable interactions of various range and (artificial) gauge fields to access i) interacting topological states of matter and ii) many-body effects in the transport properties of low-dimensional systems. In order to broaden our understanding, besides mappings onto effective models, I exploit quantum-information-inspired numerical techniques, namely Tensor Networks algorithms. In this way, insights about the entanglement structure of correlated states are also gained. In this talk, I will provide an overview of some of my recent results: in particular, I will concentrate on the Creutz-Hubbard ladder, a neat playground to address the above challenges, including the generation of flat bands as well as of non-doubled Dirac dispersion relations. In [1], I will present a theoretical analysis of the competition between correlated topological phases and orbital quantum magnetism, and the prediction of topological quantum phase transitions with different underlying conformal field theories (CFTs). In [2], I will examine the response of an interacting system of Dirac-Weyl fermions confined in a one-dimensional (1D) ring: i will show that the tuning of repulsive interactions leads to a unique many-body system that displays an enhancement of the Drude weight—the zero-frequency peak in the ac conductivity—with respect to the non-interacting value. Finally, I will review our proposal to experimentally realize this model in a synthetic ladder, made of two internal states of ultracold fermionic atoms in a one-dimensional optical lattice. References: [1] J. Jünemann, et al., PRX 7, 031057 (2017) [2] M. Bischoff, et al., PRB 96, 241112(R) (2017)

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Matteo Rizzi, University of Mainz
SR 0.03 TP
Contact: David Gross