Role of disorder in the Mott-Hubbard transition

We investigate the role of disorder in the Mott-Hubbard transition based on the slave-rotor representation of the Hubbard model, where an electron is decomposed into a fermionic spinon for a spin degree of freedom and a bosonic rotor (chargon) for a charge degree of freedom. In the absence of disorder the Mott-Hubbard insulator is assumed to be the spin liquid Mott insulator in terms of gapless spinons near the Fermi surface and gapped chargons interacting via U(1) gauge fields. We found that the Mott-Hubbard critical point becomes unstable as soon as disorder is turned on. As a result, a disorder critical point appears to be identified with the spin liquid glass insulator to the Fermi liquid metal transition, where the spin liquid glass consists of the U(1) spin liquid and the chargon glass. We expect that glassy behaviors of charge fluctuations can be measured by the optical spectra in the insulating phase of an organic material $\kappa-(BEDT-TTF)_{2}Cu_{2}(CN)_{3}$. Furthermore, since the Mott-Anderson critical point depends on the spinon conductivity, universality in the critical exponents may not be found.