Winding number statistics of a parametric chiral unitary random matrix ensemble

Petr Braun, Nico Hahn, Daniel Waltner, Omri Gat, Thomas Guhr

Research output: Contribution to journalArticlepeer-review


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.

Original languageAmerican English
Article number224011
JournalJournal of Physics A: Mathematical and Theoretical
Issue number22
StatePublished - 7 Jun 2022


  • chiral symmetry
  • random matrix theory
  • topological condensed matter
  • winding number

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • General Physics and Astronomy
  • Statistics and Probability
  • Mathematical Physics
  • Modelling and Simulation


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