The Mott (metal-insulator) transition occurs in d-metal compounds owing to strong Coulomb interaction (electron correlations). More often, this transition occurs in antiferromagnetic phase (so-called Slater scenario), but the situation changes for magnetically frustrated systems: only paramagnetic metallic and insulator states are involved, a spin liquid being formed. The transition into such insulator state is related to correlation-induced Hubbard splitting (the Mott scenario). In the Mott state the gap in the spectrum is essentially the charge gap determined by boson excitation branch. Therefore the electrons become fractionalized: the spin degrees of freedoms are determined by neutral fermions (spinons), and charge ones by bosons. The corresponding slave-boson representation was first introduced by Anderson.

In fact, bosons and fermions are coupled by a gauge field, so that the problem of confinement occurs. The transition into the metallic confinement state is described as a Bose condensation, the electron Green's function acquiring finite residue. On the other hand, in the deconfinement insulator state the bosons have a gap, so that the spectrum is incoherent (the full electron Green's function is a convolution of boson and fermion ones) and includes Hubbard's bands.

New theoretical developments provided a topological point of view for the Mott transition, since spin liquid possesses topological order. Phase transitions in frustrated systems can be treated in terms of topological excitations (instantons, monopoles, visons, vortices) which play a crucial role for confinement.

To describe the Mott transition we use the Kotliar-Ruckenstein slave-boson representation which provides explicitly the spectrum of both Hubbard bands. In the absence of considerable quasimomentum dependence of spinon distribution function (a localized spin phase without fermion hopping), the corresponding self-energy tends to zero. However, for a spin liquid we have a sharp Fermi surface. Thus for the Mott insulators the spinon Fermi surface is expected to be preserved even in the insulating phase, so that the Luttinger theorem (conservation of the volume under the Fermi surface) remains valid. However, this Fermi surface is strongly temperature dependent since a characteristic scale of spinon energies is small in comparison with that of electron ones. Thus the spectrum picture in the insulating state is considerably influenced by the spinon spin-liquid spectrum and hidden Fermi surface.

V.Yu  Irkhin
JETP Letter 117, issue 1 (2023)