Winding number statistics of a parametric chiral unitary random matrix ensemble
Abstract
The winding number is a concept in complex analysis which has, in the presence of chiral symmetry, a physics interpretation as the topological index belonging to gapped phases of fermions. We study statistical properties of this topological quantity. To this end, we set up a random matrix model for a chiral unitary system with a parametric dependence. We analytically calculate the discrete probability distribution of the winding numbers, as well as the parametric correlations functions of the winding number density. Moreover, we address aspects of universality for the twopoint function of the winding number density by identifying a proper unfolding procedure. We conjecture the unfolded twopoint function to be universal. *Dedicated to the Memory of Fritz Haake.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 June 2022
 DOI:
 10.1088/17518121/ac66a9
 arXiv:
 arXiv:2112.14575
 Bibcode:
 2022JPhA...55v4011B
 Keywords:

 random matrix theory;
 topological condensed matter;
 chiral symmetry;
 winding number;
 Mathematical Physics
 EPrint:
 20 pages, 2 figures