Band-Insulator-Metal-Mott-Insulator transition in the half--filled $t-t^{\prime}$ ionic-Hubbard chain

TL;DR

This paper explores the phase transitions in a half-filled $t-t^{\prime}$ ionic-Hubbard chain, revealing complex insulator-metal-insulator transitions driven by electron interactions and hopping parameters using bosonization.

Contribution

It provides a detailed phase diagram of the $t-t^{\prime}$ ionic-Hubbard model, identifying multiple transition types and phases depending on the next-nearest-hopping amplitude.

Findings

Identification of three insulating phases: band, ferroelectric, and Mott insulators.

Discovery of a metallic phase emerging between insulators for certain parameters.

Characterization of phase transitions as second-order and Kosterlitz-Thouless types.

Abstract

We investigate the ground state phase diagram of the half-filled $t-t^{\prime}$ repulsive Hubbard model in the presence of a staggered ionic potential $\Delta$, using the continuum-limit bosonization approach. We find, that with increasing on-site-repulsion $U$, depending on the value of the next-nearest-hopping amplitude $t^{\prime}$, the model shows three different versions of the ground state phase diagram. For $t^{\prime} < t^{\prime}_{\ast}$, the ground state phase diagram consists of the following three insulating phases: Band-Insulator at $U<U_{c}$, Ferroelectric Insulator at $U_{c} < U < U_{s}$ and correlated (Mott) Insulator at $U > U_{c}$. For $t^{\prime} > t^{\prime}_{c}$ there is only one transition from a spin gapped metallic phase at $U<U_{c}$ to a ferroelectric insulator at $U > U_{c}$. Finally, for intermediate values of the next-nearest-hopping amplitude $t^{\prime}_{\ast} < t^{\prime} < t^{\prime}_{c}$ we find that with increasing on-site repulsion, at $U_{c1}$ the model undergoes a second-order commensurate-incommensurate type transition from a band insulator into a metallic state and at larger $U_{c2}$ there is a Kosterlitz-Thouless type transition from a metal into a ferroelectric insulator.