Local topology for periodic Hamiltonians and fuzzy tori
arXiv:2403.18931
Abstract
A variety of local index formulas is constructed for 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.
Corrections mainly in Section 5. To be published in Mathematical Physics, Analysis and Geometry