# Algebraic localization implies exponential localization in non-periodic insulators

@article{Lu2021AlgebraicLI, title={Algebraic localization implies exponential localization in non-periodic insulators}, author={Jianfeng Lu and Kevin D. Stubbs}, journal={arXiv: Mathematical Physics}, year={2021} }

Exponentially-localized Wannier functions are a basis of the Fermi projection of a Hamiltonian consisting of functions which decay exponentially quickly in space. In two and three spatial dimensions, it is well understood for periodic insulators that exponentially-localized Wannier functions exist if and only if there exists an orthonormal basis for the Fermi projection with finite second moment (i.e. all basis elements satisfy $\int |\boldsymbol{x}|^2 |w(\boldsymbol{x})|^2 \,\text{d…

## 4 Citations

Algebraic localization of Wannier functions implies Chern triviality in non-periodic insulators

- Mathematics
- 2021

For gapped periodic systems (insulators), it has been established that the insulator is topologically trivial (i.e., its Chern number is equal to 0) if and only if its Fermi projector admits an…

FINITE SECOND MOMENT IMPLIES CHERN TRIVIALITY IN NON-PERIODIC INSULATORS

- Mathematics
- 2021

Abstract. For gapped periodic systems (insulators), it has been established that the insulator is topologically trivial (i.e., its Chern number is equal to 0) if and only if its Fermi projector…

Existence and computation of generalized Wannier functions for non-periodic systems in two dimensions and higher

- MathematicsArchive for Rational Mechanics and Analysis
- 2022

This work identifies an assumption under which it is proved that ELWFs can be constructed as the eigenfunctions of a sequence of self-adjoint operators acting on the Fermi projection and numerically verifies that the construction yields ELWF in various cases where this assumption holds.

Localised Module Frames and Wannier Bases from Groupoid Morita Equivalences

- Mathematics
- 2021

Following the operator algebraic approach to Gabor analysis, we construct frames of translates for the Hilbert space localisation of the Morita equivalence bimodule arising from a groupoid…

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