Distinct critical behaviors from the same state in quantum spin and population dynamics perspectives
Name
PhysRevE.103.012106.pdf
Description
Published version
Size
774.64 KB
Format
Adobe PDF
Checksum (MD5)
81c6dca409b46f97982e6aa660a7e639
Author(s)
Baldwin, CL
Shivam, S
Sondhi, SL
Kardar, M
Date Issued
2021
Journal
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
Abstract
© 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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PHYSREVE.103.012106
