10 research outputs found
Scaling theory of the Mott-Hubbard metal-insulator transition in one dimension
We use the Bethe ansatz equations to calculate the charge stiffness of the one-dimensional
repulsive-interaction Hubbard model for electron densities close to the Mott
insulating value of one electron per site (), where is the ground
state energy, is the circumference of the system (assumed to have periodic
boundary conditions), and is the magnetic flux
enclosed. We obtain an exact result for the asymptotic form of
as at , which defines and yields an analytic expression for
the correlation length in the Mott insulating phase of the model as a
function of the on-site repulsion . In the vicinity of the zero temperature
critical point U=0, , we show that the charge stiffness has the
hyperscaling form , where and is a universal scaling function which we calculate. The
physical significance of in the metallic phase of the model is that it
defines the characteristic size of the charge-carrying solitons, or {\em
holons}. We construct an explicit mapping for arbitrary and 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 of a result previously obtained using a weak- coupling
approximation, and implies hole-like transport for .Comment: 34 pages, REVTEX (5 figures by request