Hydrodynamics in lattice models with continuous non-Abelian symmetries

TL;DR

This paper develops an effective field theory for hydrodynamics in lattice systems with continuous non-Abelian symmetries, explaining diffusion behaviors and differences from other conservation laws across various models.

Contribution

It introduces a systematic hydrodynamic framework for non-Abelian symmetries on lattices, clarifying ensemble independence and diffusion characteristics in diverse physical systems.

Findings

Hydrodynamics with non-Abelian symmetries are described by coupled noisy diffusion equations.

The framework explains qualitative differences between flavor symmetry and other non-Abelian conservation laws.

Numerical and theoretical analysis shows conventional spin diffusion in non-integrable SU(2) spin chains.

Abstract

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.