一维排斥费米子中自旋-电荷分离的出现和破缺
Emergence and disruption of spin-charge separation in one-dimensional repulsive fermions
摘要：
在低温下，一维（1D）相互作用费米子的集体激发表现出自旋-电荷分离，这是Tomonaga-Luttinger液体（TLL）理论预测的独特特征，但严格的理解仍然具有挑战性。本文利用热力学Bethe Answer（TBA）方法，解析地导出了具有任意相互作用强度的一维排斥自旋1/2费米气体的普适性质。我们展示了自旋电荷分离是如何从确切的TBA形式主义中出现的，以及它是如何被两个自由度之间的相互作用所破坏的，这使我们超越了TLL范式。基于精确的激发谱，我们进一步计算了自旋和电荷的动力学结构因子。DSFs的峰表现出可区分的自旋和电荷的传播速度作为相互作用强度的函数，这可以通过超冷原子的布拉格光谱观察到。
英文摘要：
At low temperature, collective excitations of one-dimensional (1D) interacting fermions exhibit spin-charge separation, a unique feature predicted by the Tomonaga-Luttinger liquid (TLL) theory, but a rigorous understanding remains challenging. Using the thermodynamic Bethe Ansatz (TBA) formalism, we analytically derive universal properties of a 1D repulsive spin-1/2 Fermi gas with arbitrary interaction strength. We show how spin-charge separation emerges from the exact TBA formalism, and how it is disrupted by the interplay between the two degrees of freedom which brings us beyond the TLL paradigm. Based on the exact low-lying excitation spectra, we further evaluate the spin and charge dynamical structure factors (DSFs). The peaks of the DSFs exhibit distinguishable propagating velocities of spin and charge as functions of interaction strength, which can be observed by Bragg spectroscopy with ultracold atoms.
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