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A Computational Non-commutative Geometry Program for Disordered Topological Insulators

Part of the SpringerBriefs in Mathematical Physics Book Series (volume 23)

DOI: 10.1007/978-3-319-55023-7

ISBN: 978-3-319-55022-0

Publisher: Springer International Publishing - Springer Journals

Mar 18, 2017

1 - 9 of 9 Chapters

Available

Disordered Topological Insulators: A Brief Introduction

Prodan, Emil

Pages: 1 –9

[Our main goal for this Chapter is to introduce the periodic table of topological insulators and superconductors (see Table 1.1). Since the physical principles behind this table involve the robustness of certain physical properties against disorder, we will take a short detour and introduce first...
Available

Electron Dynamics: Concrete Physical Models

Prodan, Emil

Pages: 11 –24

[This Chapter introduces and characterizes the so called lattice models, which integrate naturally in the general framework for homogeneous materials introduced in Chap. 1. It also fixes the notations and the conventions used throughout. A model of disorder is introduced and the various regimes...
Available

Non-commutative Brillouin Torus

Prodan, Emil

Pages: 25 –48

[In this Chapter, we review the fundamental theoretical tools, starting with the space of disordered configurations and its associated dynamical systems, the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}...
Available

Auxiliary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document}-Algebras

Prodan, Emil

Pages: 49 –61

[This Chapter introduces and characterizes the approximating algebras used later to define the canonical finite-volume approximations and to analyze the numerical errors. In particular, the approximating finite algebra generates the ordinary finite super-cell models with periodic boundary...
Available

Canonical Finite-Volume Algorithms

Prodan, Emil

Pages: 63 –69

[As we have seen in Sect. 3.8, the response functions and the various thermodynamic coefficients are expressed as correlation functions of the type: 5.1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}...
Available

Error Bounds for Smooth Correlations

Prodan, Emil

Pages: 71 –77

[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...
Available

Applications: Transport Coefficients at Finite Temperature

Prodan, Emil

Pages: 79 –98

[In the first part of the Chapter, we show that the non-commutative Kubo-formula for the transport coefficients is covered by the theory developed so far. In the second part, we present computer assisted calculations of the finite-temperature transport coefficients, for model Hamiltonians...
Available

Error Bounds for Non-smooth Correlations

Prodan, Emil

Pages: 99 –107

[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}...
Available

Applications II: Topological Invariants

Prodan, Emil

Pages: 109 –118

[This Chapter reports computer assisted calculations of the topological invariants for strongly disordered models of topological insulators from class A and AIII in the classification Table 1.1. The computations are based on the canonical finite-volume algorithm presented in Chap. 5. The...

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