SKM 2023 – wissenschaftliches Programm
DY 9.7: Vortrag
Montag, 27. März 2023, 15:45–16:00, MOL 213
Winding Number Statistics for Parametric Chiral Random Matrices — •Nico Hahn1, Mario Kieburg2, Omri Gat3, and Thomas Guhr1 — 1University of Duisburg-Essen — 2University of Melbourne — 3The Hebrew University of Jerusalem
The winding number is a concept in complex analysis which has, in the presence of chiral symmetry, a physics interpretation as the topological invariant belonging to gapped phases of Fermions. We analytically study the statistical properties of this topological quantity. To this end, we set up a random matrix model for a chiral system with a parametric dependence. We address two chiral symmetry classes, the chiral unitary class without any further symmetries and the chiral symplectic class with additional time reversal symmetry. These classes are referred to as AIII and CII in the tenfold way of topological insulators and superconductors.