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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 1: Many-body Theory I

MP 1.4: Talk

Monday, March 18, 2024, 10:40–11:00, HL 001

A Topological Classification of Time Reversal Symmetric Frustrated Systems and Metamaterials — •Shayan Zahedi — Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, D-50937 Köln

Inspired by a paper by Roychowdhury and Lawler, we classify time reversal symmetric frustrated systems and metamaterials, guided by the Bott-Kitaev classification of topological insulators and superconductors, homotopically. This is done by investigating the topology of the space of rigidity matrices which mediate between linearised degrees of freedom and ground state constraints of frustrated systems and metamaterials.

We impose canonical time reversal symmetry on rigidity matrices and obtain Z₂-equivariant iterated loop spaces of complex Stiefel manifolds whose sets of path components are our sought for topological invariants. In the presence of canonical time reversal symmetry, our computations reveal novel topological invariants beyond those in the Bott-Kitaev periodic table. The symmetry impositions on our rigidity matrices lead to Z₂-equivariance conditions introducing the three symmetry classes AIII, AIII/BDI and AIII/CII depending on the existence and type of canonical time reversal symmetry.

We achieve such a classification by extending some of the methods used to construct the Bott-Kitaev periodic table for topological insulators and superconductors from Hermitian matrices to non-Hermitian matrices, such as the flattening of singular values of rigidity matrices.

Keywords: Frustrated systems and metamaterials; Topological classification; Rigidity matrices; Classifying loop spaces; Pyrochlore Heisenberg antiferromagnet