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“Numerical determination of Chern numbers and critical exponents for Anderson localization in tight-binding and related models”

  • Author(s): Talkington, Spenser
  • Advisor(s): Roy, Rahul
  • et al.
Abstract

Computational modules were developed to numerically determine electronic band structures, berry curvatures, Chern numbers, localization lengths, and critical exponents for tight- binding and related models. These modules were applied to a variety tight-binding and related models including the Hofstadter Model, Anderson Model, and the Chalker- Coddington model. When analytic solutions were available, numeric energy bands agreed with analytic solutions to within machine precision. In addition Chern numbers for well known models were reproduced, and localization lengths and critical exponents agreed with values in the literature.

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