Fracton magnetohydrodynamics

Abstract

We extend recent work on hydrodynamics with global multipolar symmetries -- known as "fracton hydrodynamics" -- to systems in which the multipolar symmetries are gauged. We refer to the latter as "fracton magnetohydrodynamics", in analogy to conventional magnetohydrodynamics (MHD), which governs systems with gauged charge conservation. We show that fracton MHD arises naturally from higher-rank Maxwell's equations and in systems with one-form symmetries obeying certain constraints; while we focus on "minimal" higher-rank generalizations of MHD that realize diffusion, our methods may also be used to identify other, more exotic hydrodynamic theories (e.g., with magnetic subdiffusion). In contrast to semi-microscopic derivations of MHD, our approach elucidates the origin of the hydrodynamic modes by identifying the corresponding higher-form symmetries. Being rooted in symmetries, the hydrodynamic modes may persist even when the semi-microscopic equations no longer provide an accurate description of the system.

44 pages, 2 figures; "Microscopic Hamiltonians" section added in v2

References in corpus (12)

• Generalized Global Symmetries
• Local stabilizer codes in three dimensions without string logical operators
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Three dimensional resonating valence bond liquids and their excitations
• Gapless Bosonic Excitation without symmetry breaking: Novel Algebraic Spin liquid with soft Gravitons
• Fracton topological phases from strongly coupled spin chains
• Non-Abelian hydrodynamics and the flow of spin in spin-orbit coupled substances
• Fracton hydrodynamics without time-reversal symmetry
• Universal subdiffusion in strongly tilted many-body systems
• Hilbert space shattering and dynamical freezing in the quantum Ising model
• Novel Algebraic Boson Liquid phase with soft Graviton excitations
• Kinetically Constrained Models

Cited by in corpus (10)

• Ergodicity breaking provably robust to arbitrary perturbations
• A Chern-Simons theory for dipole symmetry
• A symmetry principle for gauge theories with fractons
• Fracton superfluid hydrodynamics
• Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models
• Multipole groups and fracton phenomena on arbitrary crystalline lattices
• Anomalous hydrodynamics with triangular point group in 2 + 1 dimensions
• Filling constraints on translation invariant dipole conserving systems
• Fractonic self-duality and covariant magnetic fractons
• Collective dynamics in holographic fractonic solids