Anomalous Dynamics and Equilibration in the Classical Heisenberg Chain

Abstract

The search for departures from standard hydrodynamics in many-body systems has yielded a number of promising leads, especially in low dimension. Here we study one of the simplest classical interacting lattice models, the nearest-neighbour Heisenberg chain, with temperature as tuning parameter. Our numerics expose strikingly different spin dynamics between the antiferromagnet, where it is largely diffusive, and the ferromagnet, where we observe strong evidence either of spin super-diffusion or an extremely slow crossover to diffusion. This difference also governs the equilibration after a quench, and, remarkably, is apparent even at very high temperatures.

4+3 pages, 4+5 figures

References in corpus (11)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Exact scaling functions for one-dimensional stationary KPZ growth
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• The one-dimensional KPZ equation and its universality class
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Emergent hydrodynamics in a strongly interacting dipolar spin ensemble
• Stability of superdiffusion in nearly integrable spin chains
• Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians
• Spin crossovers and superdiffusion in the one-dimensional Hubbard model
• Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices
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Cited by in corpus (22)

• Anomalous transport from hot quasiparticles in interacting spin chains
• Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains
• Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability
• Diffusion constants from the recursion method
• Bridging the gap between classical and quantum many-body information dynamics
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• 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
• Efficient computation of cumulant evolution and full counting statistics: application to infinite temperature quantum spin chains
• Domain wall dynamics in classical spin chains: free propagation, subdiffusive spreading, and soliton emission
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
• Subdiffusive spin transport in disordered classical Heisenberg chains
• Prethermalization in periodically-driven nonreciprocal many-body spin systems
• Fluctuations of stochastic charged cellular automata
• Diagnosing quantum transport from wave function snapshots
• Dynamic scaling and Family-Vicsek universality in $SU(N)$ quantum spin chains
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Anomalous relaxation of density waves in a ring-exchange system
• Semiclassical analysis of spin dynamics in the non-Hermitian Hubbard model
• Lindblad quantum dynamics from correlation functions of classical spin chains
• Adiabaticity enhancement in the classical transverse field Ising chain, and its effective non-Hermitian description