远离微扰区的少体问题的精确数值解法
Numerically exact approach to few-body problems far from a perturbative regime
摘要：
超冷气体实验技术的最新发展为在量子水平上研究从“少”到“多”的跃迁开辟了一条途径。在这种情况下，粒子间关联的精确描述是非常重要的，因为据信它们可以被量子工程师用于量子精密测量、量子测温学、量子热机、{ \it等}。不幸的是，这些相关性的理论描述是非常具有挑战性的，因为它们远远超出了任何变分方法。相比之下，精确的多体描述由于多体希尔伯特空间的指数增长而迅速达到数值限制。在这项工作中，我们刷了一个非常有效的方法来构造一个多体基，它起源于物理论证。我们表明，在一个简单的截止常用的方法相比，它使一个非常有限的数值资源进行精确的计算。作为例子，我们研究系统中的无自旋玻色子和两个组件的费米子的混合物被限制在一个一维的谐波陷阱远离微扰制度的量子关联。
英文摘要：
Recent developments of experimental techniques in the field of ultra-cold gases open a path to study the crossover from 'few' to 'many' on the quantum level. In this case, accurate description of inter-particle correlations is very important since it is believed that they can be utilized by quantum engineers in quantum metrology, quantum thermometry, quantum heat engines, {\it etc}. Unfortunately, a theoretical description of these correlations is very challenging since they are far beyond any variational approaches. By contrast, the exact many-body description rapidly hits numerical limitations due to an exponential increase of the many-body Hilbert space. In this work, we brush up a very effective method of constructing a many-body basis which originates in the physical argumentation. We show that, in contrast to the commonly used approach of a straightforward cut-off, it enables one to perform exact calculations with very limited numerical resources. As examples, we study quantum correlations in systems of spinless bosons and two-component mixtures of fermions confined in a one-dimensional harmonic trap being far from the perturbative regime.
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