Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential.
Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential.
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DOI：
10.1126/sciadv.1500197
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发表时间：
2015-07
期刊：
影响因子：
13.6
通讯作者：
Parish MM
中科院分区：
文献类型：
--
作者：
Levinsen J;Massignan P;Bruun GM;Parish MM
给出了单个杂质与一维囚禁量子气体强相互作用的近似精确解。精确描述强相互作用的量子多体系统是现代物理学中的一大挑战。一维系统提供了基本的洞察力，因为它们往往服从于精确的方法。然而，对于实验上相关的外部约束情况，还没有确切的解决方案。我们给出了一维费米气体在无限短程排斥极限附近的简谐势的一个强大的Ansatz。对于费米海中单一杂质的情况，我们证明了在少数和多体极限下，我们的ANSATZ与数值上的精确结果是无法区分的。在此基础上，我们进一步推导出了一个有效的海森伯自旋链模型，该模型适用于任何自旋混合物，我们在该模型中解析地得到了杂质本征态。特别是，在基态波函数的表达式中出现了经典的帕斯卡三角。除了为强关联物理学提供一个重要的基准之外，我们的结果还与新兴的量子技术相关，在这些技术中，对一维量子态的精确知识至关重要。
A near exact solution is revealed for a single impurity strongly interacting with a one-dimensional trapped quantum gas. A major challenge in modern physics is to accurately describe strongly interacting quantum many-body systems. One-dimensional systems provide fundamental insights because they are often amenable to exact methods. However, no exact solution is known for the experimentally relevant case of external confinement. We propose a powerful ansatz for the one-dimensional Fermi gas in a harmonic potential near the limit of infinite short-range repulsion. For the case of a single impurity in a Fermi sea, we show that our ansatz is indistinguishable from numerically exact results in both the few- and many-body limits. We furthermore derive an effective Heisenberg spin-chain model corresponding to our ansatz, valid for any spin-mixture, within which we obtain the impurity eigenstates analytically. In particular, the classical Pascal’s triangle emerges in the expression for the ground-state wave function. As well as providing an important benchmark for strongly correlated physics, our results are relevant for emerging quantum technologies, where a precise knowledge of one-dimensional quantum states is paramount.