Chiral quantum chaos around exponentially many zero modes in the quantum breakdown model

Abstract:The quantum breakdown model is a model of randomly interacting fermions, motivated by the physics of dielectric breakdown. Here, we establish classification of symmetry and quantum chaos in a zero-dimensional, all-to-all-interacting version of the quantum breakdown model. It exhibits the $\mathbb{Z}_4$ periodicity with respect to the number of fermionic modes, reminiscent of the symmetry classification of the Sachdev-Ye-Kitaev model. A unique feature of the quantum breakdown model is that it realizes all the five classes with chiral symmetry and hosts an exponentially large number of many-body zero modes protected by the chiral index. We elucidate the separation and scaling of the spectral gap and demonstrate the symmetry-enriched hard-edge spectral statistics as signatures of quantum chaos in the chiral symmetry classes.

Strongly Correlated Electrons (cond-mat.str-el); Disordered Systems and Neural Networks (cond-mat.dis-nn); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)

arXiv:2609.39404 [cond-mat.str-el]

(or arXiv:2609.39404v1 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2609.39404 arXiv-issued DOI via DataCite (pending registration)