Winding Number Statistics for Chiral Random Matrices: Averaging Ratios of Determinants with Parametric Dependence

Abstract

Topological invariance is a powerful concept in different branches of physics as they are particularly robust under perturbations. We generalize the ideas of computing the statistics of winding numbers for a specific parametric model of the chiral Gaussian Unitary Ensemble to other chiral random matrix ensembles. Especially, we address the two chiral symmetry classes, unitary (AIII) and symplectic (CII), and we analytically compute ensemble averages for ratios of determinants with parametric dependence. To this end, we employ a technique that exhibits reminiscent supersymmetric structures while we never carry out any map to superspace.

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Cited by in corpus (5)

• 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