Distinct Critical Behaviors from the Same State in Quantum Spin and Population Dynamics Perspectives

TL;DR

This paper reveals how the same underlying mathematical structure leads to different critical behaviors in quantum spin systems and population dynamics, uncovering new physics and transitions.

Contribution

It introduces a generalized class of models linking quantum and population dynamics, showing how minor differences cause significant changes in phase transition behavior.

Findings

Discontinuous spin transitions become continuous in population models

New critical exponents emerge in population perspectives

Exact solutions and numerical results illustrate the distinct behaviors

Abstract

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 wavefunction 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 which are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions which are continuous become governed by new critical exponents. We introduce a more general class of models which 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.