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

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.

Automated summary

The deep connection between ground states of transverse-field spin systems and evolving viral populations is explored, revealing that minor differences between the two models lead to significant consequences in phase transitions and critical exponents. A more general class of models is introduced to encompass both cases, and exact solutions are obtained in a mean-field limit. Numerical results for one-dimensional chains with power-law interactions are presented, showing that treating spin models as population-dynamical models can lead to unexpected new physics and insights.