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Kitaev proposed an interacting model of spins (1/2) on a honeycomb lattice exactly solvable by mapping onto free Majorana fermions coupled to a Z_2 gauge field, hosting vortices (pi flux in a hexagon). In the presence of a time-reversal symmetry-breaking term, the ground state is gapped, characterized by a Chern number v in Z and the system hosts anyonic excitations. The Chern number ν mod 16 specifies the type of anyonic excitations, hence the sixteen-fold way. Our investigation in many well-chosen triangular vortex configurations (and their duals) shows 14 out of 16 of these phases. The phases with v = +-7 are missing. In a general case, we prove that any periodic vortex configuration with an odd number of vortices per geometric unit cell can only host even Chern numbers whereas odd Chern numbers can be found in other cases. Reference: J.N. Fuchs, S. Patil, J. Vidal, https://arxiv.org/abs/2005.03655 People interested in chatting with the speaker please let it know to Matteo Rizzi, who will organize a schedule accordingly.

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Sourabh Patil, Sorbonne University, Paris
BlueJeans
Contact: Matteo Rizzi