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

作者：Nico Hahn, Mario Kieburg, Omri Gat, Thomas Guhr · 发表于：Journal of Mathematical Physics · 年份：2023 · DOI：10.1063/5.0164352 · 被引用次数：4 · 研究领域：Random Matrices and Applications、Quantum Chromodynamics and Particle Interactions、Quantum many-body systems

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.