Correlations in one-dimensional disordered electronic systems with interaction

We investigate the effects of randomness in a strongly correlated electron model in one-dimension at half-filling. The ground state correlation functions are exactly written by products of 3$\times$3 transfer matrices and are evaluated numerically. The correlation lengths depend on randomness when the interaction is effectively weak. On the contrary, they are completely insensitive to randomness when the interaction is effectively strong.Comment: 7 pages, Revte

Orbital Liquid in Perovskite Transition-Metal Oxides

We study the effects of the degeneracy of the $e_g$ orbitals as well as the double exchange interaction with $t_{2g}$ spins in perovskite transition-metal oxides. In addition to the spin field ${\vec S}_i$, the isospin field ${\vec T}_i$ is introduced to describe the orbital degrees of freedom. The isospin is the quantum dynamical variable, and is represented by the boson with a constraint. The dispersion of this boson is flat along $(\pi/a,\pi/a,k_z)$ ($a$: lattice constant) and the other two equivalent directions. This enables the orbital disordered phase down to low temperatures. We interpret some of the anomalous experiments, i.e., optical absorption and d.c. resistivity, in the low temperature ferromagnetic phase of La$_{1-x}$Sr$_x$MnO$_3$ with $x > 0.2$ in terms of this orbital liquid picture.Comment: 4 pages, RevTex and 1 Postscript figur