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.

5 pages

References in corpus (5)

• The density-matrix renormalization group in the age of matrix product states
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Exact scaling functions for one-dimensional stationary KPZ growth
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Ballistic spin transport in a periodically driven integrable quantum system

Cited by in corpus (7)

• Kardar-Parisi-Zhang universality from soft gauge modes
• Spin crossovers and superdiffusion in the one-dimensional Hubbard model
• Coupled Hydrodynamics in Dipole-Conserving Quantum Systems
• The fractal geometry of growth: fluctuation-dissipation theorem and hidden symmetry
• Decay of spin-spin correlations in disordered quantum and classical spin chains
• Coexistence of diffusive and ballistic transport in integrable quantum lattice models
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems