论文标题
晶格中的tonks-girardeau气体的确切光谱函数
Exact spectral function of a Tonks-Girardeau gas in a lattice
论文作者
论文摘要
强相关系统的单粒子光谱函数是描述其动力学和传输特性的重要组成部分。我们开发了一种一般方法来计算Tonks-Girardeau制度中强烈相互作用的一维玻色气的确切光谱功能，对任何类型的限制电势有效，并将其应用于晶格上的玻色子，以在所有能量和动量尺度上获得完整的光谱功能。我们发现它显示了三个主要的奇异线。可以将前两个识别为均匀流体的Lieb-I和Lieb-II模式的类似物。相反，第三个特别是由于晶格的存在。我们表明，如非线性Luttinger液体描述所预测的那样，光谱函数显示了接近Lieb-I和Lieb-II奇异性的幂律行为，并获得了确切的指数。特别是，LIEB-II模式在光谱函数上显示出差异，与动态结构因子中发生的情况不同，因此提供了一种在具有Ultracold原子的实验中探测它的途径。
The single-particle spectral function of a strongly correlated system is an essential ingredient to describe its dynamics and transport properties. We develop a general method to calculate the exact spectral function of a strongly interacting one-dimensional Bose gas in the Tonks-Girardeau regime, valid for any type of confining potential, and apply it to bosons on a lattice to obtain the full spectral function, at all energy and momentum scales. We find that it displays three main singularity lines. The first two can be identified as the analogs of Lieb-I and Lieb-II modes of a uniform fluid; the third one, instead, is specifically due to the presence of the lattice. We show that the spectral function displays a power-law behaviour close to the Lieb-I and Lieb-II singularities, as predicted by the non-linear Luttinger liquid description, and obtain the exact exponents. In particular, the Lieb-II mode shows a divergence in the spectral function, differently from what happens in the dynamical structure factor, thus providing a route to probe it in experiments with ultracold atoms.
