Anisotropy-mediated reentrant localization

Abstract

We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $\sim r^{-a}$, 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 extensive numerical calculations and analytical methods show power-law localized eigenstates in the bulk of the spectrum, obeying recently discovered duality $a\leftrightarrow 2d-a$ 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.

arXiv comment21 pages, 11 figures, 75 references (in 5.5 pages) + 2 pages, 2 figures in Appendices

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• Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices
• Tuning the phase diagram of a Rosenzweig-Porter model with fractal disorder
• Probing multi-mobility edges in quasiperiodic mosaic lattices
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• Localization and fractality in disordered Russian Doll model
• Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder