Hidden quasiconservation laws in fracton hydrodynamics

Abstract

We show that the simplest universality classes of fracton hydrodynamics in more than one spatial dimension, including isotropic theories of charge and dipole conservation, can exhibit hidden "quasiconservation laws", in which certain higher multipole moments can only decay due to dangerously irrelevant corrections to hydrodynamics. We present two simple examples of this phenomenon. Firstly, an isotropic dipole-conserving fluid in the infinite plane conserves an infinite number of "harmonic multipole charges" within linear response; we calculate the decay or growth of these charges due to dangerously irrelevant nonlinearities. Secondly, we consider a model with $xy$ and $x^2-y^2$ quadrupole conservation, in addition to dipole conservation, which is described by isotropic fourth-order subdiffusion, yet has dangerously irrelevant sixth-order corrections necessary to relax the harmonic multipole charges. We confirm our predictions for the anomalously slow decay of the harmonic conserved charges in each setting by using numerical simulations, both of the nonlinear hydrodynamic differential equations, and in quantum automaton circuits on a square lattice.

15 pages, 8 figures; v2 is published version

References in corpus (10)

• Local stabilizer codes in three dimensions without string logical operators
• Hilbert Space Fragmentation and Commutant Algebras
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Breakdown of hydrodynamics below four dimensions in a fracton fluid
• Hydrodynamics of ideal fracton fluids
• Hilbert space fragmentation in a 2D quantum spin system with subsystem symmetries
• Distilling Fractons from Layered Subsystem-Symmetry Protected Phases
• Experimental realization of fragmented models in tilted Fermi-Hubbard chains
• A Duality Between U(1) Haah Code and 3D Smectic A Phase
• Vortices and Fractons

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