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

C. L. Baldwin, S. Shivam, S. L. Sondhi, M. Kardar

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number012106
JournalPhysical Review E
Issue number1
StatePublished - Jan 8 2021

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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