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ICQM Prof. Xiong-Jun Liu’s group and collaborators uncover a class of quasiperiodic mosaic models with exact mobility edges

Recently, Prof. Xiong-Jun Liu’s group at ICQM Peking University, together with Prof. Jiangong You and Prof. Qi Zhou group at Chern Institute of Mathematics, Nankai University proposed a class of exactly solvable quasiperiodic mosaic models to realize mobility edges (MEs), which are beyond the traditional models with exact ME that can only be determined by duality transformation. They also proposed a novel scheme with high feasibility to precisely realize the model based on optical Raman lattice which is of experimental feasibility. The results are published in Physical Review Letters  [Phys. Rev. Lett. 125, 196604 (2020)],  entitled “One-dimensional quasiperiodic mosaic lattice with exact mobility edges.”


Anderson localization is a fundamental quantum phenomenon in condensed matter physics, showing the disorder-induced localization of electronic wave-functions. The MEs in energy which separate extended and localized states are a most important concept in understanding the localization physics and can bring about novel quantum phenomena. For example, if the system is in metallic or insulating phase if the Fermi energy is in the extended or the localized region. Accordingly, varying the disorder strength or particle number density may shift the position of ME across Fermi energy, and induce the metal-insulator transition. Unlike the 1D disorder systems where no ME can exist, the 1D quasiperiodic systems host MEs in certain cases, e.g. in the presence of long-range hopping, additional quasiperiodic lattice potentials, and have attracted great attention in recent years. However, as a fundamental but complicate phenomenon, the ME physics are usually hard to be studied analytically. While in the very few cases the ME may be analytically determined through subtle symmetry argument, the whole models are not exactly solvable. This hinders the exact understanding of the MEs and the extended-localization transitions. Moreover, it is an even more challenging task to obtain the nontrivial models with MEs, which not only are exactly solvable, but also can be precisely realized in experiment with high feasibility. To uncover such nontrivial systems with MEs is however of general importance and is highly desired in the field of localization physics.

In this published Letter, the authors proposed a class of exactly solvable 1D mosaic models to realize MEs which can be arbitrary even number in the energy spectra, depending on the parameter, and propose a novel scheme based on optical Raman lattice to precisely realize the model in experiment. The proposed models are fundamental, with the analytical solutions providing the exact results not only for the MEs, but also for the localization and extended features of all states in the spectra, as derived with beautiful and rigorous proof (based on a Fields Medal Work in 2015). This is well beyond the existing extensive studies on this issue in the literature.  The analytical results of MEs are in excellent agreement with the numerical studies. Moreover, the high feasibility of the models in the physical realization should pave the way for experimental exploration of the predicted exact ME physics. This work combines the elegant models, beautiful analytical theory, and highly feasible experimental schemes, and shall provide important new insights into the fundamental understanding of the mobility edge and localization physics.

This work was published in Physical Review Letters  [PRL 125, 196604 (2020)]. In this work, Yucheng Wang, a postdoc at ICQM Peking University and the Institute for Quantum Science and Engineering, Southern University of Science and Technology, and  Xu Xia, a postdoc at Chern Institute of Mathematics, Nankai University, are the co-first author. Long Zhang, a postdoc at ICQM Peking University, also contributed to this work. Prof. Xiong-Jun Liu at the ICQM, Prof. Qi Zhou, and Prof. Jiangong You at Nankai University are the co-corresponding authors. This work was supported by NSFC, MOST, and CAS.