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A Computational Non-commutative Geometry Program for Disordered Topological InsulatorsError Bounds for Smooth Correlations

A Computational Non-commutative Geometry Program for Disordered Topological Insulators: Error... [In this Chapter we derive upper bounds on the error introduced by restricting to a finite-volume, and show that they decay to zero faster than any inverse power of the volume. The error bounds derived here are relevant for the finite-temperature correlation functions, which in general involve only the smooth functional calculus with the Hamiltonian. In these cases, the fast convergence to the thermodynamic limit of the numerical algorithms is not conditioned by the localized or delocalized character of the energy spectrum. This is important, for example, when studying the metal-insulator transition, where inherently the character of the spectrum changes.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Computational Non-commutative Geometry Program for Disordered Topological InsulatorsError Bounds for Smooth Correlations

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Publisher
Springer International Publishing
Copyright
© The Author(s) 2017
ISBN
978-3-319-55022-0
Pages
71 –77
DOI
10.1007/978-3-319-55023-7_6
Publisher site
See Chapter on Publisher Site

Abstract

[In this Chapter we derive upper bounds on the error introduced by restricting to a finite-volume, and show that they decay to zero faster than any inverse power of the volume. The error bounds derived here are relevant for the finite-temperature correlation functions, which in general involve only the smooth functional calculus with the Hamiltonian. In these cases, the fast convergence to the thermodynamic limit of the numerical algorithms is not conditioned by the localized or delocalized character of the energy spectrum. This is important, for example, when studying the metal-insulator transition, where inherently the character of the spectrum changes.]

Published: Mar 18, 2017

Keywords: Error Bound; Fourier Coefficient; Thermodynamic Limit; Functional Calculus; Inverse Power

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