• 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}
}
• Published 7 January 2021
• Physics
• arXiv: Mathematical Physics
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 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 • Mathematics Archive 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 ## References SHOWING 1-10 OF 30 REFERENCES 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 Optimal Decay of Wannier functions in Chern and Quantum Hall Insulators • Physics, Mathematics • 2016 We investigate the localization properties of independent electrons in a periodic background, possibly including a periodic magnetic field, as e. g. in Chern insulators and in quantum Hall systems. Exponential localization of Wannier functions in insulators. • Physics, Mathematics Physical review letters • 2007 The exponential localization of Wannier functions in two or three dimensions is proven for all insulators that display time-reversal symmetry, settling a long-standing conjecture. Our proof relies on Localization implies Chern triviality in non-periodic insulators • Physics • 2020 We investigate the relation between the localization and the topological properties of two-dimensional gapped quantum systems of independent electrons in a disordered background, including magnetic The Haldane model and its localization dichotomy. • Physics • 2018 Gapped periodic quantum systems exhibit an interesting Localization Dichotomy, which emerges when one looks at the localization of the optimally localized Wannier functions associated to the Bloch Maximally-localized Wannier Functions: Theory and Applications • Physics • 2012 The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced Analytic Properties of Bloch Waves and Wannier Functions The one-dimensional Schr\"odinger equation with a periodic and symmetric potential is considered, under the assumption that the energy bands do not intersect. The Bloch waves, Beyond Diophantine Wannier diagrams: Gap labelling for Bloch–Landau Hamiltonians • Mathematics • 2018 It is well known that, given a$2d$purely magnetic Landau Hamiltonian with a constant magnetic field$b$which generates a magnetic flux$\varphi$per unit area, then any spectral island$\sigma_b\$
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