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

TL;DR

This paper explores the existence and properties of long-lived solitons in the classical Heisenberg chain, linking them to integrable models and suggesting their role in observed KPZ scaling phenomena.

Contribution

It demonstrates the presence of long-lived solitons in a non-integrable Heisenberg chain and connects them to integrable Ishimori chain solutions, providing explicit construction methods.

Findings

Long-lived solitons exist in the Heisenberg chain.

Solitons are related to Ishimori chain solutions.

Solitons may explain KPZ scaling in the model.

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.