Dresden 2026 – scientific programme
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MA: Fachverband Magnetismus
MA 59: Magnonics III
MA 59.10: Talk
Friday, March 13, 2026, 12:00–12:15, POT/0361
Z Topological Index for 3D Hamiltonians based on Lattice Gauge Theory — Nastaran Salehi and •Manuel Pereiro — Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden
The characterization of topological phases in three-dimensional (3D) systems often requires extending concepts well-established in two dimensions (2D). We propose a robust method for calculating an integer topological invariant, akin to the Chern number, for 3D Hamiltonians with periodic boundary conditions. This approach utilizes conceptual elements derived from lattice gauge theory, defining the invariant over a discretized Brillouin zone (a 3-torus, T3). By constructing U(1) link variables from the Bloch wavefunctions, we define a gauge-invariant quantity from Wilson loops over elementary 3D plaquettes (cubes) in k-space. The resulting topological index is an integer, reflecting the classification of principal fiber bundles T3 × U(1) and related to the homotopy group π3(P2(R)) ≅ Z. This method is general and computationally efficient, avoids issues with band degeneracies, and provides a unique integer invariant for each band. We adapt the method for magnetic Hamiltonians and showcase its effectiveness with two examples: firstly, a 3D Kagome lattice model, and secondly, a realistic material, Mn3Se, for which the magnon spectra is obtained by employing electronic structure first-principles calculations.
Keywords: Lattice Gauge theory; Topological magnon transport; Kagome 3D magnet