SCALING THEORY OF THE MOTT-HUBBARD METAL-INSULATOR-TRANSITION IN ONE-DIMENSION

We use the Bethe ansatz equations to calculate the charge stiffness D(c) = (L/2)d2E0/dPHI(c)2\PHI(c) = 0 of the one-dimensional repulsive-interaction Hubbard model for electron densities close to the Mott insulating value of one electron per site (n = 1), where E0 is the ground-state energy, L is the circumference of the system (assumed to have periodic boundary conditions), and (hc/e)PHI(c) is the magnetic flux enclosed. We obtain an exact result for the asymptotic form of D(c)(L) as L --> infinity at n = 1, which defines and yields an analytic expression for the correlation length xi in the Mott insulating phase of the model as a function of the on-site repulsion U. In the vicinity of the zero-temperature critical point U = 0, n = 1, we show that the charge stiffness has the hyperscaling from D(c)(n, L, U) = Y+ (xidelta, xi/L), where delta = \1 - n\ and Y+ is a universal scaling function which we calculate. The physical significance of xi in the metallic phase of the model is that it defines the characteristic size of the charge-carrying solitons, or holons, We construct an explicit mapping for arbitrary U and xidelta much less than 1 of the holons onto weakly interacting spinless fermions, and use this mapping to obtain an asymptotically exact expression for the low-temperature thermopower near the metal-insulator transition, which is a generalization to arbitrary, U of a result previously obtained using a weak-coupling approximation, and implies holelike transport for 0 < 1 - n much less than xi-1.