Exact solutions for two interacting particles in a one-dimensional ring with a magnetic flux

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Abstract
We solve the one-dimensional extended Hubbard model with a magnetic flux analytically for the case of two particles. We find that bound states are ground states only for attractive interactions. We have studied the variation of the ground-state energy as a function of the flux. For the bound state, the period of the oscillation is half of a flux quantum. The dependence of the magnitude of the energy barrier on the size of the ring is discussed in connection with the possible existence of the flux quantization in the thermodynamic limit.