Variational description of Mott insulators: the case of the one-dimensional $t{-}t^\prime$ Hubbard model

The Gutzwiller wave function for a strongly correlated system can, if supplemented with a long-range Jastrow factor, provide a proper variational description of Mott insulators. We demonstrate this concept in the prototypical one-dimensional $t-t^\prime$ Hubbard model, where at half filling we reproduce all known phases, namely the ordinary Mott undimerized insulator with power-law spin correlations at small $t^\prime/t$, the spin-gapped metal above a critical $t^\prime/t$ and small $U$, and the dimerized Mott insulator at large repulsion. Within this frame, we also recover relationships between the unprojected BCS spectrum and the spin-excitation properties, and between the long-wavelength behavior of the Jastrow term and the charge excitations.