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arXiv · 2203.12753

Spectral Form Factor of a Quantum Spin Glass

Michael Winer·Richard Barney·Christopher L. Baldwin·Victor Galitski·Brian Swingle
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Abstract

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.

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Michael Winer, Richard Barney, Christopher L. Baldwin, Victor Galitski, Brian Swingle. 2022-03-23. Spectral Form Factor of a Quantum Spin Glass. https://doi.org/10.1007/jhep09(2022)032

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