通过耗散辅助算子演进而探测流体动力学临界现象
Probing hydrodynamic crossovers with dissipation-assisted operator evolution
AI总结：
本文通过耗散辅助算子演进而研究相互作用晶格模型中扩散的出现，发现扩散常数随密度呈反比关系，且提出了一种最小模型以解释输运临界现象。
摘要：
通过人工耗散来抑制纠缠增长，我们绘制了在不同U(1)电荷密度下，一个通用相互作用晶格模型中扩散出现的图景。我们追踪了从弹道输运到扩散输运的临界行为，发现扩散常数D与低密度ρ成反比。我们的数值方法推广了耗散辅助算子演进（DAOE）算法：在BBGKY层次的精神下，我们有效地通过集合平均近似非局域算子，而非完全丢弃它们。这大大降低了算子纠缠熵，同时仍能准确预测所有密度尺度下的扩散常数。我们进一步构建了一个最小模型以解释输运临界现象，得到的电荷相关函数与数值数据吻合良好。我们的结果澄清了守恒密度的流体动力学相关函数的主要贡献，并为低温度输运的推广提供了指导。
英文摘要：
Using artificial dissipation to tame entanglement growth, we chart the emergence of diffusion in a generic interacting lattice model for varying U(1) charge densities. We follow the crossover from ballistic to diffusive transport above a scale set by the scattering length, finding the intuitive result that the diffusion constant scales as $D \propto 1/ρ$ at low densities $ρ$. Our numerical approach generalizes the Dissipation-Assisted Operator Evolution (DAOE) algorithm: in the spirit of the BBGKY hierarchy, we effectively approximate non-local operators by their ensemble averages, rather than discarding them entirely. This greatly reduces the operator entanglement entropy, while still giving accurate predictions for diffusion constants across all density scales. We further construct a minimal model for the transport crossover, yielding charge correlation functions which agree well with our numerical data. Our results clarify the dominant contributions to hydrodynamic correlation functions of conserved densities, and serve as a guide for generalizations to low temperature transport.
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