We present a model for alloys of compound semiconductors by introducing a one-dimensional binary random system where impurities are placed in one sublattice while host atoms lie on the other sublattice. The source of disorder is the stochastic fluctuation of the impurity energy from site to site. Although the system is one-dimensional and random, we demonstrate analytical and numerically the existence of extended states in the neighborhood of a given resonant energy, which match that of the host atoms.
We have constructed a one dimensional exactly solvable model, which is based on the t-J model of strongly correlated electrons, but which has additional quantum group symmetry, ensuring the degeneration of states. We use Bethe Ansatz technique to investigate this model. The thermodynamic limit of the model is considered and equations for different density functions written down. These equations demonstrate that the additional colour degrees of freedom of the model behave as in a gauge theory, namely an arbitrary distribution of colour indices over particles leave invariant the energy of the ground state and the excitations. The S-matrix of the model is shown to be the product of the ordinary t − J model S-matrix and the unity matrix in the colour space.
We consider exactly solvable 1D multi-band fermionic Hamiltonians, which have affine quantum group symmetry for all values of the deformation. The simplest Hamiltonian is a multi-band t − J model with vanishing spin-spin interaction, which is the affinization of an underlying XXZ model. We also find a multi-band generalization of standard t−J model Hamiltonian. 495 Mod. Phys. Lett. A 1998.13:495-503. Downloaded from www.worldscientific.com by FLINDERS UNIVERSITY LIBRARY on 02/07/15. For personal use only.
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