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

• Main Authors: Baldwin, CL (Author), Shivam, S (Author), Sondhi, SL (Author), Kardar, M (Author)
• Format: Article
• Language: English
• Published: American Physical Society (APS), 2022-04-20T18:06:01Z.
• Subjects: Article
• Online Access: Get fulltext

 © 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.