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Topological Lattice Defects by Groupoid Methods and Kasparov's KK-Theory - MaRDI portal

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Topological Lattice Defects by Groupoid Methods and Kasparov's KK-Theory

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Publication:6364582

DOI10.1088/1751-8121/AC254AzbMATH Open1520.81135arXiv2104.02029MaRDI QIDQ6364582

Author name not available (Why is that?)

Publication date: 5 April 2021

Abstract: The bulk-boundary and a new bulk-defect correspondence principles are formulated using groupoid algebras. The new strategy relies on the observation that the groupoids of lattices with boundaries or defects display spaces of units with invariant accumulation manifolds, hence they can be naturally split into disjoint unions of open and closed invariant sub-sets. This leads to standard exact sequences of groupoid Cast-algebras that can be used to associate a Kasparov element to a lattice defect and to formulate an extremely general bulk-defect correspondence principle. As an application, we establish a correspondence between topological defects of a 2-dimensional square lattice and Kasparov's group KK1(Cast(mathbbZ3),mathbbC). Numerical examples of non-trivial bulk-defect correspondences are supplied.





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