Abstract Spin-density (charge) separation, marked by distinct propagation velocities of spin and density excitations, epitomizes strong correlations, historically confined to one-dimensional (1D) systems. The recent experimental work of https: //doi. org/10. 1038/s41586-025-09016-9S. Dhar, B. Wang, M. Horvath, { et al. Nature 642, 53 (2025) }, using a weakly interacting 3D Bose-Einstein condensate of ^133Cs atoms confined in a 2D optical lattice to realize spin-density separation and demonstrate boson anyonization, motivates a deeper exploration into how dimensionality and interactions govern quantum correlations. In this work, we investigate this in two-component bosonic mixtures with finite-range interactions, probing 1D and 3D dynamics. Using path integral effective field theory within the one-loop approximation, we derive analytical expressions for zero-temperature ground-state energy and quantum depletion, seamlessly recovering contact interaction results in the contact limit. By crafting an effective action for decoupled density and spin modes, we compute dynamic structure factors (DSFs), revealing how finite-range interactions sculpt spin-density separation. A pivotal finding is the dimensionality-driven divergence in DSF peak dynamics: in 1D, peaks ascend to higher frequencies with increasing interaction strength, yielding sharp responses; in 3D, peaks descend to lower frequencies, with broader density wave profiles. These insights highlight dimensionality's critical role in collective excitations and provide a robust theoretical blueprint for probing interaction-driven quantum phenomena via Bragg spectroscopy, paving new pathways for exploring dimensionally tuned quantum correlations in ultracold quantum gases.
Ye et al. (2025) studied this question.