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.

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

References in corpus (18)

• Anderson Transitions
• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Coherent many-body spin dynamics in a long-range interacting Ising chain
• Photonics meets excitonics: natural and artificial molecular aggregates
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Many-Body Delocalization in Strongly Disordered System with Long-Range Interactions: Finite Size Scaling
• Self-dual quasiperiodic systems with power-law hopping
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• Can many-body localization persist in the presence of long-range interactions or long-range hopping?
• Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
• Robustness of delocalization to the inclusion of soft constraints in long-range random models
• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Emergent fractal phase in energy stratified random models
• Non-ergodic delocalized phase with Poisson level statistics
• Universal algebraic growth of entanglement entropy in many-body localized systems with power-law interactions
• Renormalization to localization without a small parameter
• Localization and fractality in disordered Russian Doll model

Cited by in corpus (13)

• Emergent fractal phase in energy stratified random models
• 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
• Coexistence of extended and localized states in finite-sized mosaic Wannier-Stark lattices
• Emergent multifractality in power-law decaying eigenstates
• Reentrant localization transition induced by a composite potential
• Fractal states of the Schwinger model
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping
• Anderson localisation in spatially structured random graphs
• Robust Correlation-Induced Localization Under Time-Reversal Symmetry Breaking
• Localization and fractality in disordered Russian Doll model
• Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder