Winding number statistics of a parametric chiral unitary random matrix ensemble*Dedicated to the Memory of Fritz Haake. (7th June 2022)

• Record Type: Journal Article
• Authors: Braun, Petr; Hahn, Nico; Waltner, Daniel; Gat, Omri; Guhr, Thomas
• Is Part Of: Journal of physics. Volume 55:Number 22(2022)
• Publication Date: 2022-06-07
• Subjects: random matrix theory -- topological condensed matter -- chiral symmetry -- winding number; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ac66a9
• Languages: English
• ISSNs: 1751-8113

Abstract

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 two-point function of the winding number density by identifying a proper unfolding procedure. We conjecture the unfolded two-point function to be universal.