Quadrupole-conserving dynamics in the non-commutative plane

Abstract

Inspired by ``fracton hydrodynamic" universality classes of dynamics with unusual conservation laws, we present a new dynamical universality class that arises out of local area-preserving dynamics in the non-commutative plane. On this symplectic manifold, the area-preserving spatial symmetry group $\mathrm{SL}(2,\mathbb{R})⋊{\mathbb{R}}^2$ is a symmetry group compatible with non-trivial many-body dynamics. The conservation laws associated to this symmetry group correspond to the dipole and quadrupole moments of the particles. We study the unusual dynamics of a crystal lattice subject to such symmetries, and argue that the hydrodynamic description of lattice dynamics breaks down due to relevant nonlinearities. Numerical simulations of classical Hamiltonian dynamical systems with this symmetry are largely consistent with a tree-level effective field theory estimate for the endpoint of this instability.

19 pages, 7 figures

References in corpus (19)

• Fractons
• A Theory of Trotter Error
• Fracton Phases of Matter
• Null energy condition and superluminal propagation
• Fracton hydrodynamics
• Anomalous Diffusion in Dipole- and Higher-Moment Conserving Systems
• Subdiffusion and heat transport in a tilted 2D Fermi-Hubbard system
• Relativistic Fluids, Superfluids, Solids and Supersolids from a Coset Construction
• Towards classification of Fracton phases: the multipole algebra
• Anomalous Subdiffusion from Subsystem Symmetries
• Hidden quasiconservation laws in fracton hydrodynamics
• Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation
• Infinite families of fracton fluids with momentum conservation
• Fracton hydrodynamics without time-reversal symmetry
• Hydrodynamics of dipole-conserving fluids
• Multipole groups and fracton phenomena on arbitrary crystalline lattices
• Noncommutative Field Theory of the Tkachenko Mode: Symmetries and Decay Rate
• Dissipative fracton superfluids
• Noncommutative gauge symmetry in the fractional quantum Hall effect