论文标题
系统的$ 1/c $ - 外形总和，用于Lieb-Liniger模型中的动态相关性
A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
论文作者
论文摘要
我们介绍了一个框架，用于在任意能量本特征中计算Lieb-Liniger模型中的动态相关性，并在所有时空和时间中，将Lehmann代表与$ 1/C $扩展相结合。 The $n^{\rm th}$ term of the expansion is of order $1/c^n$ and takes into account all $\lfloor \tfrac{n}{2}\rfloor+1$ particle-hole excitations over the averaging eigenstate.重要的是，与“裸露” $ 1/c $扩展相比，它在时空均匀。该框架是基于一种方法，用于采用表现出不可综合奇点的形式因素的热力学限制。我们希望我们的框架适用于任何本地运营商。 我们确定了此扩展的前三个术语，并获得了密度密度动力学相关性的显式表达式和订单$ 1/c^2 $的动态结构因子。我们将其应用于量子淬火后的有限温度平衡状态和非平衡稳态。我们恢复了（非线性）Luttinger液体理论和在适当范围内的广义流体动力学的预测，并能够对其计算亚领校正。
We introduce a framework for calculating dynamical correlations in the Lieb-Liniger model in arbitrary energy eigenstates and for all space and time, that combines a Lehmann representation with a $1/c$ expansion. The $n^{\rm th}$ term of the expansion is of order $1/c^n$ and takes into account all $\lfloor \tfrac{n}{2}\rfloor+1$ particle-hole excitations over the averaging eigenstate. Importantly, in contrast to a 'bare' $1/c$ expansion it is uniform in space and time. The framework is based on a method for taking the thermodynamic limit of sums of form factors that exhibit non integrable singularities. We expect our framework to be applicable to any local operator. We determine the first three terms of this expansion and obtain an explicit expression for the density-density dynamical correlations and the dynamical structure factor at order $1/c^2$. We apply these to finite-temperature equilibrium states and non-equilibrium steady states after quantum quenches. We recover predictions of (nonlinear) Luttinger liquid theory and generalized hydrodynamics in the appropriate limits, and are able to compute sub-leading corrections to these.
