2022/05/19 by Xiaoming Cai, Cai, Xiaoming, Yi-Cong Yu +1
Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Quantum many-body systems #Surface and Thin Film Phenomena #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2205.09486
openalex publication_date 2022/05/19 · openalex created_date 2022/05/23 · openalex updated_date 2026/07/28
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-André-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-André-Harper models. Moreover, we show that the exact ME is related to the one in the dual model which has long-range hoppings.