Spin–charge separation

In condensed matter physics, spin–charge separation is an unusual behavior of electrons in some materials in which they 'split' into three independent particles, the spinon, the orbiton and the holon (or chargon). The electron can always be theoretically considered as a bound state of the three, with the spinon carrying the spin of the electron, the orbiton carrying the orbital degree of freedom and the chargon carrying the charge, but in certain conditions they can become deconfined and behave as independent particles.

The theory of spin–charge separation originates with the work of Sin-Itiro Tomonaga who developed an approximate method for treating one-dimensional interacting quantum systems in 1950. This was then developed by Joaquin Mazdak Luttinger in 1963 with an exactly solvable model which demonstrated spin–charge separation. In 1981 F. Duncan M. Haldane generalized Luttinger's model to the Tomonaga–Luttinger liquid concept whereby the physics of Luttinger's model was shown theoretically to be a general feature of all one-dimensional metallic systems. Although Haldane treated spinless fermions, the extension to spin-½ fermions and associated spin–charge separation was clear so that the promised follow-up paper did not appear.

Spin–charge separation is one of the most unusual manifestations of the concept of quasiparticles. This property is counterintuitive, because neither the spinon, with zero charge and spin half, nor the chargon, with charge minus one and zero spin, can be constructed as combinations of the electrons, holes, phonons and photons that are the constituents of the system. It is an example of fractionalization, the phenomenon in which the quantum numbers of the quasiparticles are not multiples of those of the elementary particles, but fractions.

Since the original electrons in the system are fermions, one of the spinon and chargon has to be a fermion, and the other one has to be a boson. One is theoretically free to make the assignment in either way, and no observable quantity can depend on this choice. The formalism with bosonic chargon and fermionic spinon is usually referred to as the "slave-fermion" formalism, while the formalism with fermionic chargon and bosonic spinon is called the "Schwinger boson" formalism. Both approaches have been used for strongly correlated systems, but neither has been proved to be completely successful. One difficulty of the spin–charge separation is that while spinon and chargon are not gauge-invariant quantities, i.e. unphysical objects, there are no direct physical probes to observe them. Therefore more often than not one has to use thermal dynamical or macroscopic techniques to see their effects. This implies that which formalism we choose is irrelevant to real physics, so in principle both approaches should give us the same answer. The reason we obtain radically different answers from these two formalisms is probably because of the wrong mean field solution we choose, which means that we are dealing with the spin–charge separation in a wrong way.

The same theoretical ideas have been applied in the framework of ultracold atoms. In a two-component Bose gas in 1D, strong interactions can produce a maximal form of spin–charge separation.