Universality classes of area-preserving dynamics

We investigate a novel dynamical universality class inspired by fracton hydrodynamics, and protected by unusual conservation laws. This class emerges from a unique symmetry algebra that non-trivially extends beyond previously classified multipolar symmetry algebras. The “multipolar” symmetry group in two spatial dimensions is characterized as the semi-direct product of R² and SL(2,R), and is realizable in microscopic models whose dynamics preserves the area of a deforming shape. We conduct large-scale numerical simulations of such dynamics in the non-commutative two-dimensional plane, studying the dynamics of a distorted two-dimensional triangular lattice and extracting dynamical critical exponents associated with the new universality class.