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The degree of localization of the Harper-Hofstadter model is shown to display striking periodic dependence on phase degrees of freedom, which can depend on the nature of the boundary condition, reminiscent of the Aharonov-Bohm effect. In the context of implementation in a finite ring-shaped lattice structure, this phase dependence can be utilized as a fundamentally different principle for precision sensing of rotation and magnetic fields based on localization rather than on interferometry.
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This content will become publicly available on February 5, 2026
Extremal principle for the Harper-Hofstadter model
We present an optimization principle for the Harper-Hofstadter model that naturally yields the critical value 𝜆=2 for the Harper parameter. We provide proofs for this principle and its corollaries. We demonstrate that it can be applied to a continuum model, where it can be used to find the physical parameters for criticality.
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- Award ID(s):
- 2309025
- PAR ID:
- 10601194
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review B
- Volume:
- 111
- Issue:
- 7
- ISSN:
- 2469-9950
- Page Range / eLocation ID:
- 075405
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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