一维哈伯德模型中的自旋交叉和超扩散
Spin crossovers and superdiffusion in the one-dimensional Hubbard model
摘要：
我们使用工具，从可积性和广义流体力学研究有限温度动力学的一维哈伯德模型。首先，我们研究电荷，自旋和能量传输远离半填充和零磁化，集中在强耦合制度，我们确定了丰富的温度和能量尺度的相互作用，不同的动力学制度之间的交叉。我们确定了一个中间温度制度类似于自旋不相干的Luttinger液体，其中自旋自由度是热的，但电荷自由度是在低温下。我们证明，自旋德鲁德重量表现出尖锐的功能，在这个政权和低温Luttinger液体政权之间的交叉，这是不存在的电荷和能量响应，并合理化这种行为的性质Bethe anomalous准粒子。然后，我们转向沿着特殊的线在相图中对应于半填充和/或零磁化的动力学，在一般的理由，我们预计，运输是亚弹道，但superdiffusive。我们提供了分析和数值证据的Kardar-Parisi-Zhang（KPZ）的动力学标度（长度和时间尺度相关的通过$x\sim t^{2/3}$）沿这两条线和在$SO(4)$对称点，它们相交。我们的研究结果表明，自旋相干交叉和KPZ缩放可以在近期的实验与光晶格哈伯德模拟器访问。
英文摘要：
We use tools from integrability and generalized hydrodynamics to study finite-temperature dynamics in the one-dimensional Hubbard model. First, we examine charge, spin, and energy transport away from half-filling and zero magnetization, focusing on the strong coupling regime where we identify a rich interplay of temperature and energy scales, with crossovers between distinct dynamical regimes. We identify an intermediate-temperature regime analogous to the spin-incoherent Luttinger liquid, where spin degrees of freedom are hot but charge degrees of freedom are at low temperature. We demonstrate that the spin Drude weight exhibits sharp features at the crossover between this regime and the low-temperature Luttinger liquid regime, that are absent in the charge and energy response, and rationalize this behavior in terms of the properties of Bethe ansatz quasiparticles. We then turn to the dynamics along special lines in the phase diagram corresponding to half-filling and/or zero magnetization where on general grounds we anticipate that the transport is sub-ballistic but superdiffusive. We provide analytical and numerical evidence for Kardar-Parisi-Zhang (KPZ) dynamical scaling (with length and time scales related via $x\sim t^{2/3}$) along both lines and at the $SO(4)$-symmetric point where they intersect. Our results suggest that both spin-coherence crossovers and KPZ scaling may be accessed in near-term experiments with optical lattice Hubbard emulators.
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