Marvin Qi, Oliver Hart, Aaron J. Friedman, Rahul Nandkishore, Andrew Lucas
SciPost Phys. 14, 029 (2023) ·
published 8 March 2023
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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.
Paolo Glorioso, Luca V. Delacrétaz, Xiao Chen, Rahul M. Nandkishore, Andrew Lucas
SciPost Phys. 10, 015 (2021) ·
published 25 January 2021
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We develop a systematic effective field theory of hydrodynamics for many-body
systems on the lattice with global continuous non-Abelian symmetries. Models
with continuous non-Abelian symmetries are ubiquitous in physics, arising in
diverse settings ranging from hot nuclear matter to cold atomic gases and
quantum spin chains. In every dimension and for every flavor symmetry group,
the low energy theory is a set of coupled noisy diffusion equations.
Independence of the physics on the choice of canonical or microcanonical
ensemble is manifest in our hydrodynamic expansion, even though the ensemble
choice causes an apparent shift in quasinormal mode spectra. We use our
formalism to explain why flavor symmetry is qualitatively different from
hydrodynamics with other non-Abelian conservation laws, including angular
momentum and charge multipoles. As a significant application of our framework,
we study spin and energy diffusion in classical one-dimensional SU(2)-invariant
spin chains, including the Heisenberg model along with multiple
generalizations. We argue based on both numerical simulations and our effective
field theory framework that non-integrable spin chains on a lattice exhibit
conventional spin diffusion, in contrast to some recent predictions that
diffusion constants grow logarithmically at late times. We show that the
apparent enhancement of diffusion is due to slow equilibration caused by
(non-Abelian) hydrodynamic fluctuations.
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