Generalized Bose–Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
Generalized Bose–Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
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DOI：
10.1088/1751-8121/aca302
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发表时间：
2022-08
期刊：
影响因子：
--
通讯作者：
Li Yang;S. Alam;H. Pu
中科院分区：
文献类型：
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作者：
Li Yang;S. Alam;H. Pu
一维（1D）量子多体系统表现出一些特殊的性质。在本文中，我们回顾了我们在强相互作用一维旋量量子气体方面的一些工作。首先，我们讨论了一个广义的玻色-费米映射，该映射将电荷自由度映射为无自旋费米气体，将自旋自由度映射为自旋链模型。这也将强相互作用的系统映射为弱相互作用的系统，这是适用于微扰计算的。接下来，基于这种映射，我们构造了一个强相互作用系统的ansatz波函数，利用它可以方便地计算许多物理量。我们通过考虑一个谐波捕获系统的集体激励和猝灭动力学来展示这种ansatz波函数的用法。
Quantum many-body systems in one dimension (1D) exhibit some peculiar properties. In this article, we review some of our work on strongly interacting 1D spinor quantum gas. First, we discuss a generalized Bose–Fermi mapping that maps the charge degrees of freedom to a spinless Fermi gas and the spin degrees of freedom to a spin chain model. This also maps the strongly interacting system into a weakly interacting one, which is amenable for perturbative calculations. Next, based on this mapping, we construct an ansatz wavefunction for the strongly interacting system, using which many physical quantities can be conveniently calculated. We showcase the usage of this ansatz wavefunction by considering the collective excitations and quench dynamics of a harmonically trapped system.