Superdiffusion from nonabelian symmetries in nearly integrable systems

Abstract

The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is sub-ballistic at any nonzero temperature: an initially localized spin fluctuation spreads in time $t$ to a width $t^{2/3}$. This exponent, as well as the functional form of the dynamical spin correlation function, suggest that spin transport is in the Kardar-Parisi-Zhang (KPZ) universality class. However, the full counting statistics of magnetization is manifestly incompatible with KPZ scaling. A simple two-mode hydrodynamic description, derivable from microscopic principles, captures both the KPZ scaling of the correlation function and the coarse features of the full counting statistics, but remains to be numerically validated. These results generalize to any integrable spin chain invariant under a continuous nonabelian symmetry, and are surprisingly robust against moderately strong integrability-breaking perturbations that respect the nonabelian symmetry.

review article, 17 pages + refs. Comments welcome

References in corpus (20)

• Many-Body Physics with Ultracold Gases
• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Exact scaling functions for one-dimensional stationary KPZ growth
• An exact solution for the KPZ equation with flat initial conditions
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Far-from-equilibrium spin transport in Heisenberg quantum magnets
• Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Ballistic spin transport in a periodically driven integrable quantum system
• Kardar-Parisi-Zhang universality from soft gauge modes
• Universal relaxational dynamics of gapped one dimensional models in the quantum sine-Gordon universality class
• Algebraic construction of current operators in integrable spin chains
• Transport in the sine-Gordon field theory: from generalized hydrodynamics to semiclassics
• Domain wall dynamics in the Landau--Lifshitz magnet and the classical-quantum correspondence for spin transport
• Density dynamics in translationally invariant spin-1/2 chains at high temperatures: a current auto-correlation approach to finite time- and length-scales
• Spin crossovers and superdiffusion in the one-dimensional Hubbard model
• Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
• Current operators in integrable spin chains: lessons from long range deformations
• Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain

Cited by in corpus (14)

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• Parametrically long lifetime of superdiffusion in non-integrable spin chains
• Partial yet definite emergence of the Kardar-Parisi-Zhang class in isotropic spin chains
• Efficient computation of cumulant evolution and full counting statistics: application to infinite temperature quantum spin chains
• KPZ fluctuations in finite volume
• Emergent random matrix universality in quantum operator dynamics
• Scaling of diffusion constants in perturbed easy-axis Heisenberg spin chains
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Dynamics of spin helices in the diluted one-dimensional $XX$ model
• Tunable superdiffusion in integrable spin chains using correlated initial states
• Superdiffusive transport in chaotic quantum systems with nodal interactions
• Nontrivial damping of magnetization currents in perturbed spin chains
• Transport in a System with a Tower of Quantum Many-Body Scars
• Effects of intertube dipole-dipole interactions in nearly integrable one-dimensional ${}^{162}$Dy gases