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We investigate interaction-driven integer quantum Hall states realized inLandau levels of monolayer graphene when two out of its four nearly degeneratespin-valley flavors are filled. By employing a model that accounts forinteractions beyond pure delta-functions as well as Zeeman andsubstrate-induced valley potentials, we demonstrate the existence of a delicatecompetition of several phases with spontaneous generation of spin-valleyentanglement, akin to the spontaneous appearance of spin-orbit coupling drivenby interactions. We encounter a particular phase that we term theentangled-Kekul\'{e}-antiferromagnet (E-KD-AF) which only becomes spin-valleyentangled under the simultaneous presence of Zeeman and substrate potentials,because it gains energy by simultaneously canting in the spin and valleyspaces, by combining features of a canted anti-ferromagnet and a cantedKekul\'{e} state. We quantify the degree of spin-valley entanglement of themany competing phases by computing their bipartite concurrence.

Spin-valley entangled quantum Hall states in graphene