Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains

Abstract

Finite temperature spin transport in integrable isotropic spin chains is known to be superdiffusive, with dynamical spin correlations that are conjectured to fall into the Kardar-Parisi-Zhang (KPZ) universality class. However, integrable spin chains have time-reversal and parity symmetries that are absent from the KPZ/stochastic Burgers equation, which force higher-order spin fluctuations to deviate from standard KPZ predictions. We put forward a non-linear fluctuating hydrodynamic theory consisting of two coupled stochastic modes: the local spin magnetization and its effective velocity. Our theory fully explains the emergence of anomalous spin dynamics in isotropic chains: it predicts KPZ scaling for the spin structure factor but with a symmetric, quasi-Gaussian, distribution of spin fluctuations. We substantiate our results using matrix-product states calculations.

New version : new derivation of the two-model NLFH, introduction of Burgers decoupling

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Cited by in corpus (22)

• Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
• Generalized hydrodynamics: a perspective
• Full Counting Statistics of Charge in Chaotic Many-body Quantum Systems
• Dynamical criticality of magnetization transfer in integrable spin chains
• Kardar-Parisi-Zhang scaling in the Hubbard model
• Diffusive hydrodynamics from long-range correlations
• Slow crossover from superdiffusion to diffusion in isotropic spin chains
• 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
• Landau-Lifschitz magnets: exact thermodynamics and transport
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• Quantum turnstiles for robust measurement of full counting statistics
• Diffusive charge transport in the gapped 1D Hubbard model at all finite temperatures
• Finite-temperature transport in the gapped spin-1/2 XXZ chain and one-dimensional lattice spinless fermion model
• Diagnosing quantum transport from wave function snapshots
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Superdiffusion resilience in Heisenberg Chains with 2D interactions on a quantum processor
• Correlations of density and current fluctuations in single-file motion of hard spheres and in driven lattice gas with nearest-neighbor interaction
• Exact Spectral Function of One-Dimensional Bose Gases
• Symmetry-based nonlinear fluctuating hydrodynamics in one dimension
• Universal scaling of higher-order cumulants in quantum isotropic spin chains