Hydrodynamics in lattice models with continuous non-Abelian symmetries

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.

arXiv comment30 pages, 22 figures. v2: 32 pages, 25 figures, added sec. 6.4 with explanation of the apparent enhancement of diffusion

References in corpus (62)

• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• How Algebraic Bethe Ansatz works for integrable model
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Spin diffusion from an inhomogeneous quench in an integrable system
• Fracton hydrodynamics
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Relativistic Hydrodynamics with General Anomalous Charges
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• Anomalous Diffusion in Dipole- and Higher-Moment Conserving Systems
• Super-diffusion in one-dimensional quantum lattice models
• Subdiffusion and heat transport in a tilted 2D Fermi-Hubbard system
• Towards classification of Fracton phases: the multipole algebra
• Hydrodynamic Fluctuations, Long-time Tails, and Supersymmetry
• Sub-ballistic growth of Rényi entropies due to diffusion
• Kinetically constrained freezing transition in a dipole-conserving system
• Towards a statistical theory of transport by strongly-interacting lattice fermions
• Semi-classical transport theory for non-Abelian plasmas
• Hydrodynamic long-time tails after a quantum quench
• Holography and hydrodynamics with weakly broken symmetries
• Anomalous spin diffusion in one-dimensional antiferromagnets
• Holographic nonlinear hydrodynamics from AdS/CFT with multiple/non-Abelian symmetries
• Universal spin dynamics in infinite-temperature one-dimensional quantum magnets
• Effective field theory for dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current
• Dissipative hydrodynamics in superspace
• Superdiffusion from emergent classical solitons in quantum spin chains
• Non-Abelian hydrodynamics and the flow of spin in spin-orbit coupled substances
• Real-time pion propagation in finite-temperature QCD
• Kardar-Parisi-Zhang universality from soft gauge modes
• Theory of diffusive fluctuations
• Light-cone spreading of perturbations and the butterfly effect in a classical spin chain
• Diffusive and precessional spin dynamics in a two-dimensional electron gas with disorder: a gauge theory view
• Kardar-Parisi-Zhang physics in integrable rotationally symmetric dynamics on discrete space-time lattice
• Anomalous relaxation and the high-temperature structure factor of XXZ spin chains
• Domain wall dynamics in the Landau--Lifshitz magnet and the classical-quantum correspondence for spin transport
• Observation of quantum-limited spin transport in strongly interacting two-dimensional Fermi gases
• Global Anomalies, Discrete Symmetries, and Hydrodynamic Effective Actions
• Heavy Operators and Hydrodynamic Tails
• Universality classes of spin transport in one-dimensional isotropic magnets: the onset of logarithmic anomalies
• Spin crossovers and superdiffusion in the one-dimensional Hubbard model
• Macroscopic Diffusive Transport in a Microscopically Integrable Hamiltonian System
• Topological sigma models & dissipative hydrodynamics
• Chern-Simons Reduction and non-Abelian Fluid Mechanics
• A panoply of Schwinger-Keldysh transport
• The coset construction for non-equilibrium systems
• Transport and hydrodynamics in the chiral limit
• The second law of thermodynamics from symmetry and unitarity
• Integrable Matrix Models in Discrete Space-Time
• Universal subdiffusion in strongly tilted many-body systems
• Nonlinear Fluctuating Hydrodynamics for the Classical XXZ Spin Chain
• Universal Spin Transport and Quantum Bounds for Unitary Fermions
• Breakdown of Diffusion on the Edge
• Holographic Non-Abelian Charged Hydrodynamics from the Dynamics of Null Horizons
• Spin diffusion in one-dimensional classical Heisenberg mode
• Odd Parity Transport In Non-Abelian Superfluids From Symmetry Locking
• Emergent entropy production and hydrodynamics in quantum many-body systems
• A New Approach to Non-Abelian Hydrodynamics
• Stochastic growth in time dependent environments
• Undular diffusion in nonlinear sigma models
• Vortices and Fractons
• Logarithmic superdiffusion in two dimensional driven lattice gases

Cited by in corpus (45)

• Finite-temperature transport in one-dimensional quantum lattice models
• Superdiffusion in spin chains
• Breakdown of hydrodynamics below four dimensions in a fracton fluid
• Stability of superdiffusion in nearly integrable spin chains
• Spectral statistics in constrained many-body quantum chaotic systems
• Spontaneous breaking of multipole symmetries
• Hydrodynamic projections and the emergence of linearised Euler equations in one-dimensional isolated systems
• Noncommuting conserved charges in quantum thermodynamics and beyond
• Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation
• Generalized hydrodynamics: a perspective
• Anomalous transport from hot quasiparticles in interacting spin chains
• Operator backflow and the classical simulation of quantum transport
• Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains
• Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices
• Roadmap on Quantum Thermodynamics
• Anomalous Dynamics and Equilibration in the Classical Heisenberg Chain
• Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability
• Fracton superfluid hydrodynamics
• Hydrodynamics in long-range interacting systems with center-of-mass conservation
• Fracton magnetohydrodynamics
• The Schwinger-Keldysh Coset Construction
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Hydrodynamic effective field theories with discrete rotational symmetry
• Absence of superdiffusion in certain random spin models
• Less is more: more scattering leading to less resistance
• Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models
• Nonlinear Response in Diffusive Systems
• Corrections to diffusion in interacting quantum systems
• Multipole groups and fracton phenomena on arbitrary crystalline lattices
• Long-lived Solitons and Their Signatures in the Classical Heisenberg Chain
• Slow crossover from superdiffusion to diffusion in isotropic spin chains
• Parametrically long lifetime of superdiffusion in non-integrable spin chains
• Non-Fermi Liquids from Dipolar Symmetry Breaking
• Holographic Schwinger-Keldysh field theory of SU(2) diffusion
• A Bound on Thermalization from Diffusive Fluctuations
• Superdiffusive magnetization transport in the XX spin chain with non-local dephasing
• Dissipative fracton superfluids
• Hydrodynamics of quantum spin liquids
• Spontaneous Symmetry Breaking, Spectral Statistics, and the Ramp
• Open-system spin transport and operator weight dissipation in spin chains
• Inhomogeneous SU(2) symmetries in homogeneous integrable U(1) circuits and transport
• Noise Induced Universal Diffusive Transport in Fermionic Chains
• Extended nonergodic regime and spin subdiffusion in disordered SU(2)-symmetric Floquet systems
• Chiral phase transition: effective field theory and holography
• Lindblad quantum dynamics from correlation functions of classical spin chains