从贝特安纳伯格的观点看一维的临界现象
Critical phenomena in one dimension from a Bethe ansatz perspective
摘要：
本文简要回顾了冷原子一维可积量子气体中量子临界现象的理论研究进展。本文讨论了几种典型的精确解模型的量子相变、普适热力学、标度函数和关联，如Lieb-Liniger玻色气体、自旋为1的反铁磁自旋-自旋相互作用玻色气体、两组分相互作用费米气体以及自旋为3/2的费米气体。我们证明，他们相应的贝特anquiry解决方案提供了一个精确的方式来理解量子多体物理，如量子临界性，Luttinger液体，威尔逊比，谭氏接触等，这些理论的发展产生了一个物理的角度，使用可积性发现实验可测试的现象，相互作用的玻色子和费米子超冷原子的系统局限于1D。
英文摘要：
This article briefly reviews recent theoretical developments in quantum critical phenomena in one-dimensional (1D) integrable quantum gases of cold atoms. We present a discussion on quantum phase transitions, universal thermodynamics, scaling functions and correlations for a few prototypical exactly solved models, such as the Lieb-Liniger Bose gas, the spin-1 Bose gas with antiferromagnetic spin-spin interaction, the two-component interacting Fermi gas as well as spin-3/2 Fermi gases. We demonstrate that their corresponding Bethe ansatz solutions provide a precise way to understand quantum many-body physics, such as quantum criticality, Luttinger liquids, the Wilson ratio, Tan's Contact, etc. These theoretical developments give rise to a physical perspective using integrability for uncovering experimentally testable phenomena in systems of interacting bosonic and fermonic ultracold atoms confined to 1D.
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