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Abstract

We consider a 2d dipolar system, d = 2, with the generalized dipole-dipole interaction similar to r(-a), and the power a controlled experimentally in trapped-ion or Rydberg-atom systems via their interaction with cavity modes. We focus on the dilute dipolar excitation case when the problem can be effectively considered as single-particle with the interaction providing long-range dipolar-like hopping. We show that the spatially homogeneous tilt beta of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion, a < d, unlike the models with random dipole orientation. The Anderson transitions are found to occur at the finite values of the tilt parameter beta = a, 0 < a < d, and beta = a =(a d =2), d =2 < a < d, showing the robustness of the localization at small and large anisotropy values. Both exact analytical methods and extensive numerical calculations show power-law localized eigenstates in the bulk of the spectrum, obeying recently discovered duality a <-> 2d -a of their spatial decay rate, on the localized side of the transition, a > a(AT). This localization emerges due to the presence of the ergodic extended states at either spectral edge, which constitute a zero fraction of states in the thermodynamic limit, decaying though extremely slowly with the system size.