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

20 pages, 2 figures

References in corpus (2)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topology vs. Anderson localization: non-perturbative solutions in one dimension

Cited by in corpus (6)

• Winding Number Statistics for Chiral Random Matrices: Averaging Ratios of Determinants with Parametric Dependence
• Winding Number Statistics for Chiral Random Matrices: Averaging Ratios of Parametric Determinants in the Orthogonal Case
• Statistical Topology -- Distribution and Density Correlations of Winding Numbers in Chiral Systems
• Hard edge asymptotics of correlation functions between singular values and eigenvalues
• Winding Number Statistics for Chiral Random Matrices: Universal Correlations and Statistical Moments in the Unitary Case
• Correlation functions between singular values and eigenvalues