Hidden dualities in 1D quasiperiodic lattice models

Author:

Gonçalves Miguel1,Amorim Bruno2,Castro Eduardo34,Ribeiro Pedro31

Affiliation:

1. University of Lisbon

2. University of Minho

3. Beijing Computational Science Research Center

4. University of Porto

Abstract

We find that quasiperiodicity-induced transitions between extended and localized phases in generic 1D systems are associated with hidden dualities that generalize the well-known duality of the Aubry-André model. These spectral and eigenstate dualities are locally defined near the transition and can, in many cases, be explicitly constructed by considering relatively small commensurate approximants. The construction relies on auxiliary 2D Fermi surfaces obtained as functions of the phase-twisting boundary conditions and of the phase-shifting real-space structure. We show that, around the critical point of the limiting quasiperiodic system, the auxiliary Fermi surface of a high-enough-order approximant converges to a universal form. This allows us to devise a highly-accurate method to obtain mobility edges and duality transformations for generic 1D quasiperiodic systems through their commensurate approximants. To illustrate the power of this approach, we consider several previously studied systems, including generalized Aubry-André models and coupled Moiré chains. Our findings bring a new perspective to examine quasiperiodicity-induced extended-to-localized transitions in 1D, provide a working criterion for the appearance of mobility edges, and an explicit way to understand the properties of eigenstates close to and at the transition.

Funder

European Research Council

Fundação para a Ciência e a Tecnologia

Publisher

Stichting SciPost

Subject

General Physics and Astronomy

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