Exact Solution of the strong coupling t-V model with twisted boundary conditions

We present the solution of the one-dimensional t-V model with twisted boundary conditions in the strong coupling limit, t<<V and show that this model can be mapped onto the strong coupling Hubbard chain threaded by a fictitious flux proportional to the total momentum of the charge carriers. The high energy eigenstates are characterized by a factorization of degrees of freedom associated with configurations of soliton and antisoliton domains and degrees of freedom associated with the movement of ``holes'' through these domains. The coexistence of solitons and antisolitons leads to a strange flux dependence of the eigenvalues. We illustrate the use of this solution, deriving the full frequency dependence of the optical conductivity at half-filling and zero temperature.