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<p>A variety of local index formulas is constructed for gapped quantum Hamiltonians with periodic boundary conditions. All dimensions of physical space as well as many symmetry constraints are covered, notably one-dimensional systems in Class DIII as well as two- and three-dimensional systems in Class AII. The constructions are based on several periodic variations of the spectral localizer and are rooted in the existence of underlying fuzzy tori. For these latter, a general invariant theory is developed.</p>

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Topological indices for periodic gapped Hamiltonians and fuzzy tori

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月13日

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  • Nora Doll,
  • Terry Loring,
  • Hermann Schulz-Baldes

摘要

A variety of local index formulas is constructed for gapped quantum Hamiltonians with periodic boundary conditions. All dimensions of physical space as well as many symmetry constraints are covered, notably one-dimensional systems in Class DIII as well as two- and three-dimensional systems in Class AII. The constructions are based on several periodic variations of the spectral localizer and are rooted in the existence of underlying fuzzy tori. For these latter, a general invariant theory is developed.