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Distinct critical behaviors from the same state in quantum spin and population dynamics perspectives

TitleDistinct critical behaviors from the same state in quantum spin and population dynamics perspectives
Publication TypeJournal Article
Year of Publication2021
AuthorsC.. L. Baldwin, S.. Shivam, S.. L. Sondhi, and M.. Kardar
JournalPhys. Rev. E
Volume103
Date Publishedjan
ISSN2470-0045
Abstract

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 eigen-vector of the same matrix. However, that vector is the wave-function 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 that are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions that are continuous become governed by new critical exponents. We introduce a more general class of models that 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.

DOI10.1103/PhysRevE.103.012106