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.

中文翻译：

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一维斥力费米子中自旋电荷分离的出现和破坏

在低温下，一维（1D）相互作用的费米子的集体激发表现出自旋电荷分离，这是Tomonaga-Luttinger液体（TLL）理论所预测的独特特征，但严格的理解仍然具有挑战性。使用热力学的Bethe Ansatz（TBA）形式论，我们分析得出具有任意相互作用强度的一维排斥自旋1/2费米气体的通用性质。我们展示了精确的TBA形式主义如何产生自旋电荷分离，以及如何被两个自由度之间的相互作用所破坏，这使我们超越了TLL范式。基于精确的低激发光谱，我们进一步评估了自旋和电荷动力学结构因子（DSF）。DSF的峰表现出明显的自旋和电荷传播速度，它们是相互作用强度的函数，