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

A Computational Non-commutative Geometry Program for Disordered Topological Insulators: Error... [In this Chapter we analyze correlation functions of the type: 8.1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {\mathcal T}( \partial ^{\alpha _1} G_1(h) \, \partial ^{\alpha _2} G_2(h) \ldots ) \; , \quad h \in {\mathcal A}_d \; , \end{aligned}$$\end{document}where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_i$$\end{document}’s are only piecewise continuous and the discontinuities occur inside the essential spectrum of h. We establish that, if the discontinuities occur inside the mobility gaps of h, then the canonical finite-volume algorithm presented in Chap. 5 continues to display a rapid convergence to the thermodynamic limit. Key to the error estimates is the Aizenman–Molchanov bound (Aizenman and Molchanov, Commun Math Phys 157:245–278, 1993, [2], Aizenman and Warzel, Random operators: disorder effects on quantum spectra and dynamics, 2015, [3]), which is discussed and adapted to the present context.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

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

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/lp/springer-journals/a-computational-non-commutative-geometry-program-for-disordered-zLomgqkq0y
Publisher
Springer International Publishing
Copyright
© The Author(s) 2017
ISBN
978-3-319-55022-0
Pages
99 –107
DOI
10.1007/978-3-319-55023-7_8
Publisher site
See Chapter on Publisher Site

Abstract

[In this Chapter we analyze correlation functions of the type: 8.1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {\mathcal T}( \partial ^{\alpha _1} G_1(h) \, \partial ^{\alpha _2} G_2(h) \ldots ) \; , \quad h \in {\mathcal A}_d \; , \end{aligned}$$\end{document}where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_i$$\end{document}’s are only piecewise continuous and the discontinuities occur inside the essential spectrum of h. We establish that, if the discontinuities occur inside the mobility gaps of h, then the canonical finite-volume algorithm presented in Chap. 5 continues to display a rapid convergence to the thermodynamic limit. Key to the error estimates is the Aizenman–Molchanov bound (Aizenman and Molchanov, Commun Math Phys 157:245–278, 1993, [2], Aizenman and Warzel, Random operators: disorder effects on quantum spectra and dynamics, 2015, [3]), which is discussed and adapted to the present context.]

Published: Mar 18, 2017

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