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Hydrodynamics in lattice models with continuous non-Abelian symmetries

by Paolo Glorioso, Luca V. Delacrétaz, Xiao Chen, Rahul M. Nandkishore, Andrew Lucas

Submission summary

As Contributors: Luca Delacrétaz · Paolo Glorioso · Rahul Nandkishore
Arxiv Link: (pdf)
Date submitted: 2020-11-19 18:11
Submitted by: Glorioso, Paolo
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approaches: Theoretical, Computational


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.

Current status:
Editor-in-charge assigned

Reports on this Submission

Anonymous Report 2 on 2020-11-26 Invited Report


The authors have thoroughly addressed all points raised by the referees. I strongly recommend publication in SciPost.

  • validity: high
  • significance: high
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: perfect

Anonymous Report 1 on 2020-11-21 Invited Report


I am satisfied with the changes made by the authors and the clarifications provided in their reply. I am happy to recommend the manuscript for publication.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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