Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability

Anomalous transport from hot quasiparticles in interacting spin chains

“…Plugging in this decay rate τ s ∼ s 2 into the Kubo formula (36), we find that the a.c. conductivity diverges at low frequencies, as σ(ω) ∼ | log ω|. This prediction-and more generally the idea that there is a distinction between noise that preserves SU (2) and noise that does not-are borne out by numerical studies [137,[140][141][142].…”

“…However, for few-body Hamiltonian perturbations of the Heisenberg model, it turns out that many natural perturbations are generated by bounded, quasi-local operators S. Whenever this is the case to linear order in λ, the decay rate of conserved quantities is at best λ 4 (which is well out of reach of numerics). In any case, large-scale numerical studies on classical models yield dynamics that is superdiffusive out to the longest accessible timescales [141,142].…”

Long-lived Solitons and Their Signatures in the Classical Heisenberg Chain

“…Introduction-There has been renewed interest in understanding the long-time dynamics of classical manybody systems, in particular regarding the scope of anomalous, non-diffusive, transport. A paradigmatic phenomenon is Kardar-Parisi-Zhang (KPZ) scaling [1], associated with (generalised) hydrodynamics [2][3][4][5][6][7][8][9][10] and integrability [9,[11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Recent theoretical developments have identified integrability and non-abelian symmetry as key ingredients for KPZ physics [16,[23][24][25][26][27][28].…”

“…Indeed, KPZ scaling is now established [9,16] in the integrable Ishimori chain [29], also known as the integrable lattice-Landau-Lifshitz model. Intriguingly, the simple non-integrable nearest-neighbour classical Heisenberg chain was also found to host a long-lived regime of KPZ scaling at low temperature [18], and it was subsequently noted that KPZ scaling in the Ishimori chain persists under spin-symmetry preserving perturbations [17].…”

“…Our recent observation of KPZ behaviour up to enormously large scales [18] thus raises the question: does the Heisenberg chain exhibit properties ordinarily associated with integrability? In particular, one might wonder if this phenomenology can be related to magnon dynamics or the existence of solitons, thought to be crucial for KPZ behaviour both in quantum [24,26,[41][42][43] and classical integrable 1D spin systems [9,16,17,24].…”