We propose the Luttinger model with finite-range interactions as a simple tractable example in 1+1 dimensions to analytically study the emergence of Euler-scale hydrodynamics in a quantum many-body system. This non-local Luttinger model is an exactly solvable quantum field theory somewhere between conformal and Bethe-ansatz integrable models. Applying the recent proposal of generalized hydrodynamics, we show that the model allows for fully explicit yet non-trivial solutions of the resulting Euler-scale hydrodynamic equations. Comparing with exact analytical non-equilibrium results valid at all time and length scales, we show perfect agreement at the Euler scale when the interactions are short range. A formal proof of the emergence of generalized hydrodynamics in the non-local Luttinger model is also given, and effects of long-range interactions are briefly discussed.

中文翻译：

---

非局部Luttinger模型中广义流体力学的出现

我们提出具有有限范围相互作用的Luttinger模型作为1 + 1维的简单易处理的例子，以分析研究量子多体系统中欧拉尺度流体力学的出现。这种非局部Luttinger模型是一个完全可解的量子场论，介于共形模型和Bethe-ansatz可积模型之间。应用最近提出的广义流体力学的建议，我们表明该模型可以对所得的欧拉尺度流体力学方程进行完全显式但非平凡的解。与在所有时间和长度尺度上均有效的精确分析性非平衡结果进行比较，当相互作用短时，我们在欧拉尺度上显示出完美的一致性。还给出了非局部Luttinger模型中广义流体动力学出现的形式证明，