Breakdown of hydrodynamics in the classical 1D Heisenberg model

Abstract

Extensive spin-dynamics simulations have been performed to study the dynamical behavior of the classical Heisenberg chain at infinite temperatures and long wavelengths. We find that the energy and spin show distinctly different dynamics in the isotropic system. The energy correlation function follows the classical diffusion theory prediction, namely, it decays exponentially with q 2 t. In contrast, the spin correlation function is found to decay exponentially as q 2A2 t\nt, implying a logarithmically divergent diffusion constant and the failure of the usual hydrodynamic assumptions.

Spin diffusion in the one-dimensional classical Heisenberg model

“…Another subsequent numerical work in this direction [16] however claimed that although energy diffusion is normal, spin diffusion has an anomalous behavior. [17].…”

“…Although the phenomenology of spin diffusion is an old concept [3,4], its validity in classical Heisenberg model has been vigourously debated in recent times. Although much effort [13][14][15][16][17][18][19][20] has been devoted to understand whether spin diffusion in this system is normal or anomalous, a convincing conclusion is yet to be reached. Settling this question is not only conceptually important e.g., in understanding transport properties of spin systems, but also has direct implications in routinely performed experiments e.g., NMR and ESR in magnetic compounds [5][6][7][8][9].…”

Largest Lyapunov Exponents for Lattices of Interacting Classical Spins

“…These systems have been extensively studied, e.g., in the context of the spin diffusion problem [15][16][17], but their Lyapunov spectra have not yet been computed. Finite classical spin systems are also known to exhibit nontrivial integrable limits [18].…”

Comment on ‘‘Breakdown of hydrodynamics in the classical 1D Heisenberg model’’

“…In a recent Letter [1], de Alcantara Bonfim and Reiter investigated the infinite-temperature spin dynamics of the classical isotropic Heisenberg chain with emphasis on the spin-diffusion hypothesis by extensive numerical simulations. In particular, they found that their data for the spin-correlation function C(q,t) are well fitted by…”