X. Deng, A. L. Burin, I. M. Khaymovich, “Anisotropy-mediated reentrant localization” (2022)


We consider a 2d dipolar system, d=2, with the generalized dipole-dipole interaction ∼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 β 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 β=a, 0<a<d, and β=a/(a−d/2), d/2<a<d, showing the robustness of the localization at small and large anisotropy values. Both extensive numerical calculations and analytical methods 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>aAT. 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.


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