• Corpus ID: 230799481

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… 
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