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It was recently shown that the XX central spin model is integrable in thepresence of a magnetic field perpendicular to the plane in which the couplingexists. A large number of its eigenstates are such that the central spin is notcorrelated to the environmental spins it is coupled to. In this work, we firstdemonstrate that the XX-central spin model remains integrable in the presenceof an arbitrarily oriented magnetic field. We then show that, provided thecoupling is strong enough, dark states can actually be found even in thepresence of an in-plane magnetic field. We finally provide a simple explanationof this result and demonstrate its universality for a variety of distinctdistributions of the coupling of the central spin to the various bath spins.

Strong-coupling emergence of dark states in XX central spin models