一维低能相互作用的量子液体和液滴
Quantum liquids and droplets with low-energy interactions in one dimension
摘要：
我们考虑在普遍的低能量制度相互作用的一维玻色子。相互作用由吸引和排斥部分的组合组成，可以稳定量子气体，液滴和液体。特别是，我们研究了有效的三体排斥的作用，在弱吸引力的两两相互作用的系统。它的低能描述通常被认为是等价于一个只包括非零射程的两体相互作用的模型。在这里，我们表明，在零温度下，在这两种理论的状态方程同意在低密度的整体排斥定量，在气相中，可以推断出从$S$矩阵制定的统计力学。然而，这种一致性在吸引机制中是不存在的，在吸引机制中，普适性只发生在量子液滴的长距离性质中。我们开发了分析工具来研究该理论的性质，并使用密度矩阵重整化群获得了与精确数值计算惊人的一致性。
英文摘要：
We consider interacting one-dimensional bosons in the universal low-energy regime. The interactions consist of a combination of attractive and repulsive parts that can stabilize quantum gases, droplets and liquids. In particular, we study the role of effective three-body repulsion, in systems with weak attractive pairwise interactions. Its low-energy description is often argued to be equivalent to a model including only two-body interactions with non-zero range. Here, we show that, at zero temperature, the equations of state in both theories agree quantitatively at low densities for overall repulsion, in the gas phase, as can be inferred from the $S$-matrix formulation of statistical mechanics. However, this agreement is absent in the attractive regime, where universality only occurs in the long-distance properties of quantum droplets. We develop analytical tools to investigate the properties of the theory, and obtain astounding agreement with exact numerical calculations using the density-matrix renormalization group.
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