论文标题
长寿的孤子及其在古典海森堡连锁店中的签名
Long-lived Solitons and Their Signatures in the Classical Heisenberg Chain
论文作者
论文摘要
由最近在经典铁磁海森堡链中观察到的KPZ缩放的动机，我们研究了孤子激发在该模型中的作用。我们发现，海森伯格连锁店虽然众所周知是不可融合的，但它支持了一个长期寿命的孤子家族。我们将它们连接到具有$ \ log（1+ s_i \ cdot s_j）$交互的集成式岛链的确切孤子解决方案。我们明确地构建了无限寿命的固定孤子，并为移动孤子溶液提供了绝热的施工程序，这表明当下孤子孤子在不太狭窄且不太快地移动时具有长寿的海森堡对应物。最后，我们证明了它们在海森堡链的热状态下的存在，即使典型的孤子宽度大于自旋相关长度，并认为这些激发可能是KPZ缩放的基础。
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.
