



@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 {2688,
	title = {Distinct Critical Behaviors from the Same State in Quantum Spin and Population Dynamics Perspectives},
	year = {2020},
	month = {9/10/2020},
	abstract = {<p>There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations -- within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wavefunction amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: phase transitions which are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions which are continuous become governed by new critical exponents. We introduce a more general class of models which encompasses both cases, and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies.\&nbsp;</p>},
	url = {https://arxiv.org/abs/2009.05064},
	author = {Christopher L. Baldwin and S. Shivam and S. L. Sondhi and M. Kardar}
}
