Anisotropy-mediated reentrant localization

Abstract

We consider a 2d dipolar system, d=2d=2, with the generalized dipole-dipole interaction \sim r^{-a}∼r−a, and the power aa 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 \betaβ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion, a<da<d, unlike the models with random dipole orientation. The Anderson transitions are found to occur at the finite values of the tilt parameter \beta = aβ=a, 0<a<d0<a<d, and \beta = a/(a-d/2)β=a/(a−d/2), d/2<a<dd/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-aa↔2d−a of their spatial decay rate, on the localized side of the transition, a>a_{AT}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.