Department of Theoretical Physics and MTA-BME Lendület Topology and Correlation Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary.
Department of Theoretical Physics and BME-MTA Exotic Quantum Phases Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary.
Phys Rev Lett. 2018 Aug 3;121(5):056803. doi: 10.1103/PhysRevLett.121.056803.
Motivated by recent experiments in ultracold gases, we focus on the properties of the center-of-mass coordinate of an interacting one-dimensional Fermi gas, displaying several distinct phases. While the variance of the center of mass vanishes in insulating phases such as phase-separated and charge density wave phases, it remains finite in the metallic phase, which realizes a Luttinger liquid. By combining numerics with bosonization, we demonstrate that the autocorrelation function of the center-of-mass coordinate is universal throughout the metallic phase. It exhibits persistent oscillations, and its short time dynamics reveal important features of the quantum liquid, such as the Luttinger liquid parameter and the renormalized velocity. The full counting statistics of the center of mass follows a normal distribution already for small systems. Our results apply to nonintegrable systems as well and are within experimental reach for, e.g., carbon nanotubes and cold atomic gases.
受最近超冷气体实验的启发，我们关注具有不同相的相互作用一维费米气体质心坐标的性质。当质心的方差在诸如相分离和电荷密度波等绝缘相中消失时，它在金属相中仍然是有限的，金属相实现了 Luttinger 液体。通过将数值与玻色化相结合，我们证明了质心坐标的自相关函数在整个金属相中是普遍存在的。它表现出持续的振荡，其短时间动力学揭示了量子液体的重要特征，例如 Luttinger 液体参数和重整化速度。对于小系统，质心的全计数统计已经遵循正态分布。我们的结果也适用于不可积系统，例如对于碳纳米管和冷原子气体，已经可以进行实验研究。
