Scaling Theory of Transitions between the Mott Insulator and Quantum Fluids

Critical properties of the transition between the Mott insulator and quantum fluids are investigated by using the scaling theory. The Mott insulating phase and the quantum fluid phase of bi-component systems are categorized into several types depending on the existence of order and the type of excitation spectra. The critical exponents of the transition in multicomponent systems are discussed for various combinations of metal-insulator and superfiuid-insulator transitions. For the generic transition between a genuinely multicomponent metal and the Mott insulator in d dimensions, the hyperscaling is satisfied with the correlation exponent v = 1/2d, the dynamical exponent z=2d, and the Drude weight exponent [formula omitted]. It is argued that the upper critical dimension dc satisfies dc≥2. The above exponents are compared with v=l/2, z=2t and ≥ for the transition to the band insulator. Critical properties of the energy gap, the compressibility and other quantities are also discussed.