An Exactly Solvable Model with a Tunable Mott Gap without Broken Symmetry

The 1d Hubbard model at half filling provides the only known example of a Mott Hubbard insulating state, with a Mott charge gap without any concomittant broken symmetry. Such a state has inspired much current work in correlated matter in low dimensions. We present a model, where the Mott gap can be manipulated and infact made to vanish with some parameter. Using the higher conserved currents found by Shastry in 1986 for the 1-d Hubbard model, we construct a new model {\em which does show a tunable Mott gap}. The model is given by the hamiltonian $$H = H_{Hubbard}(U) + \lambda \; I_3(U),$$ where $H_{Hubbard}$ is the Hubbard hamiltonian and $I_3$ is its third conserved current. The new model has exactly the same space time symmetries as the Hubbard model, but possesses {\em two parameters}, $U ,\; \lambda$. The phase diagram in $\lambda-U$ is explored using numerical methods and the Bethe Ansatz. It displays several interesting features including a ``superconducting'' type state. A significant role is played by a band transition at $U=0$ (similar to the Lifshitz transition), wherein the two fermi points of the Hubbard model break up into 6 Fermi points. We also find a variety of second order transitions.