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The paradigmatic condensed-matter models where zero-energy localized Majorana fermions have been studied so far have the distinguishing feature of not conserving the number of fermions. Moreover, the accepted definition of "Majorana fermion" naturally belongs to this scenario. Is it possible to discuss Majorana fermions in "canonical" particle-conserving settings? In this seminar I will present several exact and numerical results on Majorana fermions in particle-conserving scenarios. I will start from the discussion of a model for bosons and fermions where, in a proper limit, the physics of the celebrated Kitaev's chain appears. I will continue by presenting exact results on Majorana fermions in ladder models where the two legs of the system can only exchange pair of particles. Finally, I will comment on the possibility of making experiments with Majorana fermions in particle-conserving settings using cold atoms.

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Leonardo Mazza, ENS Paris
Seminarraum E0.03
Contact: Simon Trebst