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 language | English |
|---|---|
| Article number | 021901 |
| Journal | Journal of Mathematical Physics |
| Volume | 64 |
| Issue number | 2 |
| DOIs | |
| State | Published - 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).