Ortiz Martín, LauraMartín-Delgado Alcántara, Miguel Ángel2023-06-172023-06-172016-120003-491610.1016/j.aop.2016.10.008https://hdl.handle.net/20.500.14352/17766© 2017 Elsevier B.V. We acknowledge financial support from the Spanish MINECO grants FIS2012-33152, FIS2015-67411, and the CAM research consortium QUITEMAD+, Grant No. S2013/ICE-2801. The research of M.A.M.-D. has been supported in part by the U.S. Army Research Office through Grant No. W911N F-14-1-0103.We construct a new model of two-dimensional quantum spin systems that combines intrinsic topological orders and a global symmetry called flavour symmetry. It is referred as the bilayer Doubled Semion model (bDS) and is an instance of symmetry-enriched topological order. A honeycomb bilayer lattice is introduced to combine a Double Semion Topolgical Order with a global spin-flavour symmetry to get the fractionalization of its quasiparticles. The bDS model exhibits non-trival braiding self-statistics of excitations and its dual model constitutes a Symmetry-Protected Topological Order with novel edge states. This dual model gives rise to a bilayer Non-Trivial Paramagnet that is invariant under the flavour symmetry and the well-known spin flip symmetry.engjournal articlehttp://dx.doi.org/10.1016/j.aop.2016.10.008http://www.sciencedirect.comhttps://arxiv.org/pdf/1604.08656.pdfopen access53Quantized hall conductanceZero modesQuantumSuperconductorsInsulatorsStatesStatisticsParticlesVorticesFermionsFísica-Modelos matemáticos