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.

1 aBaldwin, C., L.1 aShivam, S.1 aSondhi, S., L.1 aKardar, M. uhttps://arxiv.org/abs/2009.0506401030nas a2200157 4500008004100000245006700041210006700108260001400175520054300189100001900732700002900751700001700780700001900797700001900816856003700835 2020 eng d00aStudying viral populations with tools from quantum spin chains0 aStudying viral populations with tools from quantum spin chains c3/24/20203 aWe study Eigen's model of quasi-species, characterized by sequences that replicate with a specified fitness and mutate independently at single sites. The evolution of the population vector in time is then closely related to that of quantum spins in imaginary time. We employ multiple perspectives and tools from interacting quantum systems to examine growth and collapse of realistic viral populations, specifically certain HIV proteins. All approaches used, including the simplest perturbation theory, give consistent results.

1 aShivam, Saumya1 aBaldwin, Christopher, L.1 aBarton, John1 aKardar, Mehran1 aSondhi, S., L. uhttps://arxiv.org/abs/2003.10668