Solvable Two-Band Model of Fermions

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Abstract
A two-band model of spinless fermions in one dimension is constructed. Density-density couplings, umklapp scattering, and interband transitions are included. Renormalization-group equations are derived and discussed. In addition, it is shown that with one condition on the couplings and the velocities the model may be transformed to two uncoupled sine-Gordon Hamiltonians, which makes it possible to obtain solutions in regions where the renormalization-group equations are not valid. An important property of the model is that there can be superconductivity with repulsive interactions.