Universality from a circulant symmetry

Transport in one-dimensional many-body systems is often anomalous, with conserved quantities spreading in ways that go beyond standard diffusion. Despite the microscopic complexity, their large-scale dynamics can fall into dynamical universal classes characterized by distinct dynamical exponents and scaling functions. Which universality class emerges depends on how the conserved modes interact, with symmetries imposing strong constraints on these interactions.
In this talk, I will show how a global circulant symmetry of the flux jacobian can determine the universal dynamics of a many-body system. This symmetry imposes simple selection rules on the couplings between modes and organizes most modes into pairs with degenerate velocities. By extending mode-coupling theory to account for these degeneracies, we can determine the universality class of each mode directly from the symmetry structure. Remarkably, this reveals that universality classes previously thought to require fine-tuning, including the Golden Ratio class, can arise robustly from symmetry alone. I demonstrate these predictions through numerical simulations of a multilane exclusion process.