1. hidden dualities in 1d quasiperiodic lattice models

Miguel de Jesus Mestre Gonçalves

University of Lisbon, Portugal

4 May 2021 Tue 5 pm

                                      IBS Center for Theoretical Physics of Complex Systems (PCS), Administrative Office (B349), Theory Wing, 3rd floor

                                      Expo-ro 55, Yuseong-gu, Daejeon, South Korea, 34126 Tel: +82-42-878-8633                     

Quasiperiodic systems (QPS) host a plethora of exotic properties ranging from localization to topological non-trivial states. Interest in quasiperiodic structures has been recently renewed due to their experimental relevance in optical and photonic lattices and the rise of Moiré systems.


The first steps to understanding quasiperiodic-induced localization steamed out of a celebrated 1D model, proposed by Aubry and André, that predicts a localization-delocalization transition arising simultaneously for all states in the spectrum [1]. This transition is a consequence of a special duality of the Aubry-André Hamiltonian. Later generalizations of this model give rise to single-particle mobility edges that may be highly non-trivial to determine and could only be analytically predicted in a few restricted fine-tuned models.


In this talk, we propose that the quasiperiodic-induced localization-delocalization transitions in generic 1D systems are associated with local hidden dualities that are generalizations of the Aubry-André case.


Based on this conjecture, we develop a method to compute mobility edges and duality transformations for generic QPS through their commensurate approximants. To illustrate the power of the method, mobility edges and duality transformations are obtained for a number of models, including generalized Aubry-André models [2-5] and coupled Moiré chains.


We found that different special models with exact analytical phase diagrams, including [1,2,4,5], share the same property: dualities arise from the simplest possible commensurate approximant. In these cases, the phase boundaries can be obtained in a very simple way. Remarkably, even away from these fine-tuned limits, the phase diagram may also be obtained analytically to a very good approximation in some cases. In more complex models, the method can still be applied numerically in a simple way.


Our findings provide a useful and insightful way to study quasiperiodic-induced localization-delocalization transitions in 1D, including a working criterion for their emergence and for understanding the properties of eigenstates close to the transition.


[1] S. Aubry and G. André, Ann. Isr. Phys. Soc. 3, 133 (1980)

[2] J. Biddle and S. Das Sarma, Phys. Rev. Lett. 104, 070601 (2010)

[3] J. Biddle, D. J. Priour Jr., B. Wang, and S. Das Sarma, Phys. Rev. B 83, 075105 (2011)

[4] S. Ganeshan, J. H. Pixley, and S. Das Sarma, Phys. Rev. Lett. 144, 146601 (2015)

[5] Y. Wang, X. Xia, L. Zhang, H. Yao, S. Chen, J. You, Q. Zhou, and X. J. Liu, Phys. Rev. Lett. 125, 196604 (2020)