Disordered Hubbard linear chain: Arbitrary filling

The disordered Hubbard linear chain is studied for the general case of an arbitrarily filled band. For low temperatures and small transfer integral the Hubbard chain reduces to a one-dimensional disordered Heisenberg antiferromagnet. The probability distribution of the coupling constant is found to have the form $P\left(J\right)\mathrm{}\propto \frac{1}{\left(J^{1-c}\right)}$, and has a singularity at $J=0\mathrm{}$ for $c<\mathrm{}1\mathrm{}$. The exponent $\gamma =1-c$ is studied as a function of the filling and the existence of ranges of filling which do not give a singular $P\left(J\right)\mathrm{}$ is revealed. The implications for the magnetic properties are also examined. We make connection with real materials and discuss the possibility of partial charge transfer. The effect of higher dimensionality on the main feature of the theory, the singularity in $P\left(J\right)\mathrm{}$, is also studied.