Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet

Abstract

Equilibrium spatio-temporal correlation functions are central to understanding weak nonequilibrium physics. In certain local one-dimensional classical systems with three conservation laws they show universal features. Namely, fluctuations around ballistically propagating sound modes can be described by the celebrated Kardar-Parisi-Zhang (KPZ) universality class. Can such universality class be found also in quantum systems? By unambiguously demonstrating that the KPZ scaling function describes magnetization dynamics in the SU(2) symmetric Heisenberg spin chain we show, for the first time, that this is so. We achieve that by introducing new theoretical and numerical tools, and make a puzzling observation that the conservation of energy does not seem to matter for the KPZ physics.

arXiv comment5 pages

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Cited by in corpus (163)

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• Superdiffusion from nonabelian symmetries in nearly integrable systems
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• Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation
• Ballistic-to-diffusive transition in spin chains with broken integrability
• Absence of superdiffusion in certain random spin models
• Kardar-Parisi-Zhang scaling in the Hubbard model
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• Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets
• Universal scaling of spin mixing dynamics in a strongly interacting one-dimensional Fermi gas
• Diffusive hydrodynamics from long-range correlations
• Direct Evidence for Universal Statistics of Stationary Kardar-Parisi-Zhang Interfaces
• Emergent Universal Quench Dynamics in Randomly Interacting Spin Models
• Spin diffusion in perturbed isotropic Heisenberg spin chain
• Typicality of nonequilibrium (quasi-)steady currents
• Charge-current correlation equalities for quantum systems far from equilibrium
• Coexistence of diffusive and ballistic transport in integrable quantum lattice models
• Nonequilibrium criticality driven by Kardar-Parisi-Zhang fluctuations in the synchronization of oscillator lattices
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