English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
 
 
DownloadE-Mail
  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.

Item is

Files

show Files
hide Files
:
PhysRevResearch.3.033167.pdf (Publisher version), 5MB
Name:
PhysRevResearch.3.033167.pdf
Description:
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.
OA-Status:
Not specified
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
Technical Metadata:
Copyright Date:
2021
Copyright Info:
© the Author(s). Published by the American Physical Society

Locators

show
hide
Locator:
https://arxiv.org/abs/2105.07747 (Preprint)
Description:
-
OA-Status:
Not specified
Description:
-
OA-Status:
Not specified

Creators

show
hide
 Creators:
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              

Content

show
hide
Free keywords: -
 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.

Details

show
hide
Language(s): eng - English
 Dates: 2021-05-172021-08-032021-08-19
 Publication Status: Published online
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 2105.07747
DOI: 10.1103/PhysRevResearch.3.033167
 Degree: -

Event

show

Legal Case

show

Project information

show hide
Project name : -
Grant ID : 757725
Funding program : Horizon 2020 (H2020)
Funding organization : European Commission (EC)
Project name : We thank S. Blügel, E. Koch, and V. Meden for fruitful discussions. This work was supported by the Deutsche Forschungsgemeinschaft via RTG 1995, the Swiss National Science Foundation (SNSF) and NCCR QSIT, and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy–Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1-390534769. We acknowledge support from the Max Planck New York City Center for Non-Equilibrium Quantum Phenomena. Simulations were performed with computing resources granted by RWTH Aachen University. Funding was received from the European Union's Horizon 2020 research and innovation program (ERC Starting Grant, Grant Agreement No. 757725).
Grant ID : -
Funding program : -
Funding organization : -

Source 1

show
hide
Title: Physical Review Research
Source Genre: Journal
 Creator(s):
Affiliations:
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