How electrons break into pieces inside one-dimensional matter

Free electrons (left) and interacting electrons (right) moving in a three-dimensional material. Here, interacting electrons behave just like free electrons, albeit ‘dressed’ by interactions (yellow clouds).
The collective motion of interacting electrons in a one-dimensional material.
A schematic of the dispersion of electrons in three-dimensional materials (left), compared to experimentally measured dispersion of spinons and holons in a one-dimensional material (right). The dispersion (Kim, et al. Nature Physics (2006)) was measured using angle-resolved photoemission spectroscopy, on the compound SrCuO2.
Numerical simulation of charge (upper curves) and spin (lower curves) densities in a model of 1D interacting electrons called the Hubbard model. The results show that the spin and charge propagate at different speeds, and hence separate from each other. The results are from work by Jagla, et al. Physical Review B (1993).

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