Distinct critical behaviors from the same state in quantum spin and population dynamics perspectives
Author(s)
Baldwin, CL; Shivam, S; Sondhi, SL; Kardar, M
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© 2021 American Physical Society. 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 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.
Date issued
2021Department
Massachusetts Institute of Technology. Department of PhysicsJournal
Physical Review E
Publisher
American Physical Society (APS)
Citation
Baldwin, CL, Shivam, S, Sondhi, SL and Kardar, M. 2021. "Distinct critical behaviors from the same state in quantum spin and population dynamics perspectives." Physical Review E, 103 (1).
Version: Final published version