Anisotropy-mediated reentrant localization
Xiaolong Deng, Alexander L. Burin, Ivan M. Khaymovich
SciPost Phys. 13, 116 (2022) · published 24 November 2022
- doi: 10.21468/SciPostPhys.13.5.116
- Submissions/Reports
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 exact analytical methods and extensive numerical calculations 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.
Cited by 6
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 2 Xiaolong Deng,
- 3 Alexander Burin,
- 4 5 6 Ivan M. Khaymovich
- 1 Leibniz Universität Hannover / University of Hannover
- 2 Leibniz-Rechenzentrum / Leibniz Supercomputing Centre [LRZ]
- 3 Tulane University
- 4 Max-Planck-Institut für Physik komplexer Systeme / Max Planck Institute for the Physics of Complex Systems
- 5 Nordisk Institut for Teoretisk Fysik / Nordic Institute for Theoretical Physics [NORDITA]
- 6 Федеральное государственное бюджетное учреждение науки Институт физики микроструктур Российской академии наук / Institute for Physics of Microstructures, Russian Academy of Sciences [IPM RAS]
- Bundesministerium für Bildung und Forschung / Federal Ministry of Education and Research [BMBF]
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]
- FP7 Seventh Framework Programme (FP7) (through Organization: European Commission [EC])
- National Science Foundation [NSF]
- Russian Science Foundation