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.

arXiv comment20 pages, 2 figures

References in corpus (24)

• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• New directions in the pursuit of Majorana fermions in solid state systems
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Random Matrix Theories in Quantum Physics: Common Concepts
• Periodic table for topological insulators and superconductors
• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
• Random Matrix Theory and Chiral Symmetry in QCD
• Random-matrix theory of Majorana fermions and topological superconductors
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• Topological characterization of chiral models through their long time dynamics
• Symmetry classes of disordered fermions
• A random matrix model for chiral symmetry breaking
• Topology vs. Anderson localization: non-perturbative solutions in one dimension
• The chiral phase transition in a random matrix model with molecular correlations
• An elementary rigorous proof of bulk-boundary correspondence in the generalized Su-Schrieffer-Heeger model
• Random-Matrix Theory of Parametric Correlations in the Spectra of Disordered Metals and Chaotic Billiards
• Particle-Hole Symmetries in Condensed Matter
• Derivation of an eigenvalue probability density function relating to the Poincare disk
• The Bulk-Edge Correspondence in Three Simple Cases
• Stochastic field theory for a Dirac particle propagating in gauge field disorder
• Correlations of quantum curvature and variance of Chern numbers

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