Spectral Form Factor of a Quantum Spin Glass

TitleSpectral Form Factor of a Quantum Spin Glass
Publication TypeJournal Article
Year of Publication2022
AuthorsWiner, M, Barney, R, Baldwin, CL, Galitski, V, Swingle, B
Date Published4/4/2022
KeywordsDisordered Systems and Neural Networks (cond-mat.dis-nn), FOS: Physical sciences, High Energy Physics - Theory (hep-th), Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el)

It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we investigate a third class: spin glasses. These systems are partially chaotic but do not achieve full thermalization due to large free energy barriers. We examine the level spacing statistics of a canonical infinite-range quantum spin glass, the quantum p-spherical model, using an analytic path integral approach. We find statistics consistent with a direct sum of independent random matrices, and show that the number of such matrices is equal to the number of distinct metastable configurations -- the exponential of the spin glass "complexity" as obtained from the quantum Thouless-Anderson-Palmer equations. We also consider the statistical properties of the complexity itself and identify a set of contributions to the path integral which suggest a Poissonian distribution for the number of metastable configurations. Our results show that level spacing statistics can probe the ergodicity-breaking in quantum spin glasses and provide a way to generalize the notion of spin glass complexity beyond models with a semi-classical limit.