Repulsion driven metallic phase in the ground state of the half-filled $t-t^{\prime}$ ionic Hubbard chain

An unusual metallic phase is proven to develop in the one dimensional ionic Hubbard model, at half-filling and zero magnetization, at intermediate electron-electron repulsion $U$ when second neighbors hopping is allowed and tuned close to a topological Lifshitz transition (connected with a change of the Fermi surface in the non-interacting system). The metallic state lies between a band insulator phase at low repulsion and a correlated (Mott-like) insulator phase at high repulsion. In approaching the later, the metal supports spontaneous bond charge dimerization and antiferromagnetic correlations. The ground state of the system, attainable by cold atoms in optical lattices for a wide range of the parameter $U$, is extensively explored by numerically exact density-matrix renormalization-group (DMRG) calculations. A combination of mean field and effective field theory (bosonization) provides an analytical understanding of the physical processes underlying the observed phase transitions.