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  Universality of Abelian and non-Abelian Wannier functions in generalized one-dimensional Aubry-André-Harper models

Piasotski, K., Pletyukhov, M., Weber, C. S., Klinovaja, J., Kennes, D. M., & Schoeller, H. (2021). Universality of Abelian and non-Abelian Wannier functions in generalized one-dimensional Aubry-André-Harper models. Physical Review Research, 3(3): 033167. doi:10.1103/PhysRevResearch.3.033167.

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Open Access. - ublished by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.
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© the Author(s). Published by the American Physical Society

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https://arxiv.org/abs/2105.07747 (Preprint)
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Piasotski, K.1, Author
Pletyukhov, M.1, Author
Weber, C. S.1, Author
Klinovaja, J.2, Author
Kennes, D. M.1, 3, 4, Author           
Schoeller, H.1, Author
Affiliations:
1Institut für Theorie der Statistischen Physik, RWTH Aachen and JARA - Fundamentals of Future Information Technology, ou_persistent22              
2Department of Physics, University of Basel, ou_persistent22              
3Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_2266715              
4Center for Free Electron Laser Science (CFEL), ou_persistent22              

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 Abstract: Within a Dirac model in 1+1 dimensions, a prototypical model to describe low-energy physics for a wide class of lattice models, we propose a field-theoretical version for the representation of Wannier functions, the Zak-Berry connection, and the geometric tensor. In two natural Abelian gauges we present universal scaling of the Dirac Wannier functions in terms of four fundamental scaling functions that depend only on the phase γ of the gap parameter and the charge correlation length ξ in an insulator. The two gauges allow for a universal low-energy formulation of the surface charge and surface fluctuation theorem, relating the boundary charge and its fluctuations to bulk properties. Our analysis describes the universal aspects of Wannier functions for the wide class of one-dimensional generalized Aubry-André-Harper lattice models. In the low-energy regime of small gaps we demonstrate universal scaling of all lattice Wannier functions and their moments in the corresponding Abelian gauges. In particular, for the quadratic spread of the lattice Wannier function, we find the universal result Zaξ/8, where Za is the length of the unit cell. This result solves a long-standing problem providing further evidence that an insulator is only characterized by the two fundamental length scales Za and ξ. Finally, we discuss also non-Abelian lattice gauges and find that lattice Wannier functions of maximal localization show universal scaling and are uniquely related to the Dirac Wannier function of the lower band. In addition, via the winding number of the determinant of the non-Abelian transformation, we establish a bulk-boundary correspondence for the number of edge states up to the bottom of a certain band, which requires no symmetry constraints. Our results present evidence that universal aspects of Wannier functions and of the boundary charge are uniquely related and can be elegantly described within universal low-energy theories.

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Language(s): eng - English
 Dates: 2021-05-172021-08-032021-08-19
 Publication Status: Published online
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 Rev. Type: Peer
 Identifiers: arXiv: 2105.07747
DOI: 10.1103/PhysRevResearch.3.033167
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Grant ID : 757725
Funding program : Horizon 2020 (H2020)
Funding organization : European Commission (EC)

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Title: Physical Review Research
Source Genre: Journal
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Publ. Info: College Park, Maryland, United States : American Physical Society (APS)
Pages: - Volume / Issue: 3 (3) Sequence Number: 033167 Start / End Page: - Identifier: ISSN: 2643-1564
CoNE: https://pure.mpg.de/cone/journals/resource/2643-1564