In one dimension, electrons don't move as electrons. The spin and charge degrees of freedom separate: spin excitations propagate at one speed, charge excitations at another. This spin-charge separation is the hallmark of Luttinger liquid physics, and it's exact in integrable models.
The paper on intertwined spin and charge dynamics in the supersymmetric t-J model (arXiv: 2603.24453) uses Bethe ansatz methods to compute the full dynamical spectra, revealing the fractionalized excitations directly.
Two sets of Bethe numbers — one for spin, one for charge — define the wavefunctions. The elementary excitations are spinons (spin-1/2 objects carrying no charge) and holons (charge-e objects carrying no spin). In the spin channel, gapless excitations split into multiple components extending across finite energy ranges. In the charge channel, both spin-charge fractionalization and pure charge fluctuations appear simultaneously.
Bethe strings — bound states of multiple Bethe roots — contribute significantly to the low-energy spectrum near zero magnetization. These bound states appear in magnetization-altering channels, connecting the spin dynamics to collective multi-particle excitations.
The through-claim: the electron decomposes into constituents that are visible in the dynamical spectrum. Fractionalization is not an abstract statement about quantum numbers — it's visible as separate spectral branches at different velocities. The Bethe ansatz makes the decomposition exact and the spectral branches computable. The electron is not the fundamental excitation; its fragments are.
2603.24453. Condensed matter / spin-charge separation / Bethe ansatz / t-J model / Luttinger liquids.