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Title:
Localization with and without randomness
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Abstract:
Randomness is not essential for Anderson or many-body localization, with quasiperiodic potentials being a prominent example of localization without randomness. Noninteracting particles in quasiperiodic potentials have at least phases: (i) localized in real space, (ii) diffusive, and (iii) ballistic, which is localized in momentum space and is the dual of localized in real space. The diffusive phase is clearly exhibited in numerical studies in 3D. We then ask about the stability of the phases and the critical points to added randomness. We find that randomness is irrelevant at the single-particle localization transition in 3D, but it appears to be relevant for MBL, and for single particles in the symplectic class in 2D.
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