Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case

Nico Hahn*, Mario Kieburg, Omri Gat, Thomas Guhr

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We extend our recent study of winding number density statistics in Gaussian random matrix ensembles of the chiral unitary (AIII) and chiral symplectic (CII) classes. Here, we consider the chiral orthogonal (BDI) case which is the mathematically most demanding one. The key observation is that we can map the topological problem on a spectral one, rendering the toolbox of random matrix theory applicable. In particular, we employ a technique that exploits supersymmetry structures without reformulating the problem in superspace.

Original languageEnglish
Article number111902
JournalJournal of Mathematical Physics
Volume64
Issue number11
DOIs
StatePublished - 1 Nov 2023

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