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

Abstract

Motivated by the KPZ scaling recently observed in the classical ferromagnetic Heisenberg chain, we investigate the role of solitonic excitations in this model. We find that the Heisenberg chain, although well-known to be non-integrable, supports a two-parameter family of long-lived solitons. We connect these to the exact soliton solutions of the integrable Ishimori chain with $\log (1+S_i\cdot S_j)$ interactions. We explicitly construct infinitely long-lived stationary solitons, and provide an adiabatic construction procedure for moving soliton solutions, which shows that Ishimori solitons have a long-lived Heisenberg counterpart when they are not too narrow and not too fast-moving. Finally, we demonstrate their presence in thermal states of the Heisenberg chain, even when the typical soliton width is larger than the spin correlation length, and argue that these excitations likely underlie the KPZ scaling.

4 + 6 pages, 4 + 6 figures

References in corpus (16)

• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Superuniversality of superdiffusion
• Non-Equilibrium Dynamics and Weakly Broken Integrability
• Hydrodynamics of weak integrability breaking
• Superdiffusion from emergent classical solitons in quantum spin chains
• Kardar-Parisi-Zhang universality from soft gauge modes
• Stability of superdiffusion in nearly integrable spin chains
• Domain wall dynamics in the Landau--Lifshitz magnet and the classical-quantum correspondence for spin transport
• Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion
• Universality classes of spin transport in one-dimensional isotropic magnets: the onset of logarithmic anomalies
• Hydrodynamics in lattice models with continuous non-Abelian symmetries
• Onset of many-body quantum chaos due to breaking integrability
• Weak integrability breaking: chaos with integrability signature in coherent diffusion
• Anomalous Dynamics and Equilibration in the Classical Heisenberg Chain
• Equilibration and Thermalization of Classical Systems

Cited by in corpus (10)

• Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• 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
• Subdiffusive spin transport in disordered classical Heisenberg chains
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Diagnosing quantum transport from wave function snapshots
• Semiclassical analysis of spin dynamics in the non-Hermitian Hubbard model