论文标题
自旋 - $ 1/2 $ xxz自旋链中的域壁熔化：新兴的Luttinger液体，带分形准粒子电荷
Domain-wall melting in the spin-$1/2$ XXZ spin chain: emergent Luttinger liquid with fractal quasi-particle charge
论文作者
论文摘要
在带有本地统一进化的旋转链中保存磁化$ s^{\ rm z} $，域壁状态$ \ left | \ dots \ uparrow \ uparrow \ uparrow \ uparrow \ uparrow \ uparrow \ downarrow \ downarrow \ downarrow \ downarrow \ downarrow \ downarrow \ downarrow \ downarrow \ dots \ dots \ right> $通常是“熔体”。在很大程度上，在域壁的初始位置附近的扩展区域中形成了非平凡的磁化特征。对于不可积分的动力学，熔化是扩散的，熵产生在大小$ \ sqrt {t} $的融化区域内。相比之下，当进化是可集成的时，弹道传输会占主导地位，并导致融化的区域在及时线性生长，没有广泛的熵产生：自旋链在任何时候都在零熵状态下保持本地。在这里，我们表明，对于$ 1/2 $ xxz链的可集成旋转链，熔化区域中低能的量子波动会产生一种新兴的luttinger液体，这显然与平衡相差。这种紧急Luttinger液体的引人注目的功能是其准粒子电荷（或Luttinger参数$ K $），该电荷获得了对XXZ链各向异性参数$δ$的分形依赖性。
In spin chains with local unitary evolution preserving the magnetization $S^{\rm z}$, the domain-wall state $\left| \dots \uparrow \uparrow \uparrow \uparrow \uparrow \downarrow \downarrow \downarrow \downarrow \downarrow \dots \right>$ typically "melts". At large times, a non-trivial magnetization profile develops in an expanding region around the initial position of the domain-wall. For non-integrable 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 quasi-particle charge (or Luttinger parameter $K$) which acquires a fractal dependence on the XXZ chain anisotropy parameter $Δ$.
