Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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. In particular, 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.

Original languageAmerican English
Article number021901
JournalJournal of Mathematical Physics
Volume64
Issue number2
DOIs
StatePublished - 1 Feb 2023

Bibliographical note

Funding Information:
We thank Boris Gutkin for fruitful discussions. This work was funded by the German-Israeli Foundation within the project Statistical Topology of Complex Quantum Systems (Grant No. GIF I-1499-303.7/2019) (N.H., O.G., and T.G.). Furthermore, M.K. acknowledges support by the Australian Research Council via Discovery Project Grant No. DP210102887.

Publisher Copyright:
© 2023 Author(s).

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