Exact mobility edges in Aubry-Andr\'{e}-Harper models with relative phases

Xiaoming Cai; Yi-Cong Yu

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arXiv · 2205.09486

Exact mobility edges in Aubry-Andr\'{e}-Harper models with relative phases

Xiaoming Cai·Yi-Cong Yu

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Abstract

Mobility edge (ME), a critical energy separating localized and extended states in spectrum, is a central concept in understanding the localization physics. However, there are few models with exact MEs. In the paper, we generalize the Aubry-Andr\'{e}-Harper model proposed in [Phys. Rev. Lett. 114, 146601 (2015)] and recently realized in [Phys. Rev. Lett. 126, 040603 (2021)], by introducing a relative phase in the quasiperiodic potential. Applying Avila's global theory we analytically compute localization lengths of all single-particle states and determine the exact expression of ME, which both significantly depend on the relative phase. They are verified by numerical simulations, and a physical perception of the exact expression is also provided. We further demonstrate that the exact expression of ME works for an even broad class of generalized Aubry-Andr\'{e}-Harper models. Moreover, we show that the exact ME is related to the one in the dual model which has long-range hoppings.

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Xiaoming Cai, Yi-Cong Yu. 2022-05-19. Exact mobility edges in Aubry-Andr\'{e}-Harper models with relative phases. https://arxiv.org/abs/2205.09486

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