In spin chains with local unitary evolution preserving the magnetization $S^{\mathrm{z}}$, the domain-wall state $\left|\cdots \uparrow \uparrow \uparrow \uparrow \uparrow \downarrow \downarrow \downarrow \downarrow \downarrow \cdots \right.〉$ typically “melts.” At large times, a nontrivial magnetization profile develops in an expanding region around the initial position of the domain wall. For nonintegrable dynamics, the melting is diffusive, with entropy production within a melted region of size $\sqrt{t}$. In contrast, when the evolution is integrable, ballistic transport dominates and results in a melted region growing linearly in time, with no extensive entropy production: The spin chain remains locally in states of zero entropy at any time. Here we show that, for the integrable spin-$1/2$ XXZ chain, low-energy quantum fluctuations in the melted region give rise to an emergent Luttinger liquid which, remarkably, differs from the equilibrium one. The striking feature of this emergent Luttinger liquid is its quasiparticle charge (or Luttinger parameter $K$), which acquires a fractal dependence on the XXZ chain anisotropy parameter $\mathrm{\Delta }$.

中文翻译：

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自旋12XXZ自旋链中的畴壁熔化：带有分形准粒子电荷的新兴Luttinger液体

在具有局部unit演化的自旋链中保持磁化强度 ${\mathrm{小号}}^{\mathrm{ž}}$，域墙状态 $\left|\cdots \uparrow \uparrow \uparrow \uparrow \uparrow \downarrow \downarrow \downarrow \downarrow \downarrow \cdots \right.〉$通常是“融化”。通常，在畴壁的初始位置周围的扩展区域中会产生不平凡的磁化曲线。对于不可积分的动力学，融解是扩散性的，熵的产生是在一定大小的融化区域内$\sqrt{Ť}$。相反，当演化是可积分的时，弹道运输占主导地位，并导致熔化的区域随时间线性增长，而没有大量的熵产生：自旋链在任何时候都保持局部处于零熵状态。这里我们表明，对于可积自旋$\mathrm{1个}/2$在XXZ链上，熔化区域的低能量子涨落产生了出现的Luttinger液体，该液体明显不同于平衡液体。这种新兴的Luttinger液体的显着特征是其准粒子电荷（或Luttinger参数$ķ$），它对XXZ链各向异性参数具有分形依赖性 $\mathrm{\Delta }$。