



@article {3127,
	title = {Disordered Lieb-Robinson bounds in one dimension},
	year = {2022},
	month = {8/10/2022},
	abstract = {<p>By tightening the conventional Lieb-Robinson bounds to better handle systems which lack translation invariance, we determine the extent to which \&quot;weak links\&quot; suppress operator growth in disordered one-dimensional spin chains. In particular, we prove that ballistic growth is impossible when the distribution of coupling strengths μ(J) has a sufficiently heavy tail at small J, and identify the correct dynamical exponent to use instead. Furthermore, through a detailed analysis of the special case in which the couplings are genuinely random and independent, we find that the standard formulation of Lieb-Robinson bounds is insufficient to capture the complexity of the dynamics -- we must distinguish between bounds which hold for all sites of the chain and bounds which hold for a subsequence of sites, and we show by explicit example that these two can have dramatically different behaviors. All the same, our result for the dynamical exponent is tight, in that we prove by counterexample that there cannot exist any Lieb-Robinson bound with a smaller exponent. We close by discussing the implications of our results, both major and minor, for numerous applications ranging from quench dynamics to the structure of ground states.</p>},
	keywords = {Disordered Systems and Neural Networks (cond-mat.dis-nn), FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Physics (quant-ph)},
	doi = {10.48550/ARXIV.2208.05509},
	url = {https://arxiv.org/abs/2208.05509},
	author = {Baldwin, Christopher L. and Ehrenberg, Adam and Guo, Andrew Y. and Alexey V. Gorshkov}
}
@article {3008,
	title = {Spectral Form Factor of a Quantum Spin Glass},
	year = {2022},
	month = {4/4/2022},
	abstract = {<p>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 \&quot;complexity\&quot; 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.</p>},
	keywords = {Disordered 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)},
	doi = {https://doi.org/10.48550/arXiv.2203.12753},
	url = {https://arxiv.org/abs/2203.12753},
	author = {Winer, Michael and Barney, Richard and Christopher L. Baldwin and Galitski, Victor and Swingle, Brian}
}
