# Winding number statistics of a parametric chiral unitary random matrix ensemble

@article{Braun2022WindingNS, title={Winding number statistics of a parametric chiral unitary random matrix ensemble}, author={Petr A. Braun and Nico Hahn and Daniel Waltner and Omri Gat and Thomas Guhr}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2022}, volume={55} }

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…

## One Citation

### Winding Number Statistics for Chiral Random Matrices: Averaging Ratios of Determinants with Parametric Dependence

- Mathematics
- 2022

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…

## References

SHOWING 1-10 OF 39 REFERENCES

### RANDOM MATRIX THEORY AND CHIRAL SYMMETRY IN QCD

- Physics
- 2000

▪ Abstract Random matrix theory is a powerful way to describe universal correlations of eigenvalues of complex systems. It also may serve as a schematic model for disorder in quantum systems. In this…

### Topological characterization of chiral models through their long time dynamics

- Physics
- 2017

We study chiral models in one spatial dimension, both static and periodically driven. We demonstrate that their topological properties may be read out through the long time limit of a bulk…

### Random matrix model for chiral symmetry breaking.

- PhysicsPhysical review. D, Particles and fields
- 1996

It is found that the chiral phase transition can be characterized by the dynamics of the smallest eigenvalue of the Dirac operator, which suggests an alternative order parameter which may be of relevance for lattice QCD simulations.

### Topological criticality in the chiral-symmetric AIII class at strong disorder.

- PhysicsPhysical review letters
- 2014

This work derives a covariant real-space formula for ν and shows that ν remains quantized and nonfluctuating when disorder is turned on, even though the bulk energy spectrum is completely localized.

### Correlations of quantum curvature and variance of Chern numbers

- PhysicsSciPost Physics
- 2021

We analyse the correlation function of the quantum curvature
in complex quantum systems, using a random matrix model to provide
an exemplar of a universal correlation function. We show that the…

### Symmetry Classes of Disordered Fermions

- Mathematics
- 2005

Building upon Dyson’s fundamental 1962 article known in random-matrix theory as the threefold way, we classify disordered fermion systems with quadratic Hamiltonians by their unitary and antiunitary…

### Periodic table for topological insulators and superconductors

- Physics, Mathematics
- 2009

Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a…

### Spectral density of the QCD Dirac operator near zero virtuality.

- Physics, MathematicsPhysical review letters
- 1993

The spectral properties of a random matrix model which in the large [ital N] limit embodies the essentials of the QCD partition function at low energy.