Quantum critical scaling in convective active matter

Abstract

We construct a minimal field theory for critical quantum active matter, describing a nonconserved scalar order parameter with Landau-Ginzburg ordering and self-advection. When diffusive noise dominates, higher-order quantum vertices and non-Gaussian noise fluctuations remain relevant alongside the deterministic nonlinearities, with an upper critical dimension $d_c=2$. A one-loop renormalization-group analysis in $d=2-ε$ reveals a purely dissipative fixed point, where nonlinear noise suppresses convection, and a quantum convective saddle, where interactions, convection, and non-Gaussian noise coexist. We determine the critical exponents, show that the convective regime is distinct from conventional Burgers hydrodynamics, and discuss how it could govern transient universal scaling in microscopic models of quantum active matter before a crossover to semi-classical dynamics.