We investigate the ground-state phase diagram of the half-filled $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ repulsive Hubbard model in the presence of a staggered ionic potential $\ensuremath{\Delta}$ using the continuum-limit bosonization approach. We find that with increasing on-site repulsion $U$ , depending on the value of the next-nearest-neighbor hopping amplitude ${t}^{\ensuremath{'}}$, the model shows three different versions of the ground-state phase diagram. For ${t}^{\ensuremath{'}}<{t}_{c}^{{*}^{\ensuremath{'}}}$, 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 ${t}^{\ensuremath{'}}>{t}_{c}^{\ensuremath{'}}$ 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-neighbor hopping amplitude ${t}_{c}^{{*}^{\ensuremath{'}}}<{t}^{\ensuremath{'}}<{t}_{c}^{\ensuremath{'}}$ 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 to a ferroelectric insulator.We investigate the ground-state phase diagram of the half-filled $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ repulsive Hubbard model in the presence of a staggered ionic potential $\ensuremath{\Delta}$ using the continuum-limit bosonization approach. We find that with increasing on-site repulsion $U$, depending on the value of the next-nearest-neighbor hopping amplitude ${t}^{\ensuremath{'}}$, the model shows three different versions of the ground-state phase diagram. For ${t}^{\ensuremath{'}}<{t}_{c}^{{*}^{\ensuremath{'}}}$, 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 ${t}^{\ensuremath{'}}>{t}_{c}^{\ensuremath{'}}$ 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-neighbor hopping amplitude ${t}_{c}^{{*}^{\ensuremath{'}}}<{t}^{\ensuremath{'}}<{t}_{c}^{\ensuremath{'}}$ 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 to a ferroelectric insulator.

arXiv:cond-mat/0611415Physical Review BJun 22, 200717 citations

Quantum phase diagram of the half filled Hubbard model with bond-charge interaction

A. Dobry, Armando A. Aligia

arXiv:1009.4113Nuclear Physics BOct 22, 201024 citations

Phase diagram of the one-dimensional extended ionic Hubbard model

Zhao Hong-Xia, Hui Zhao, Chen Yu-Guang +1 more

We use a density-matrix renormalization group method to study quantitatively the phase diagram of the half-filled one-dimensional (1D) extended Hubbard model in the presence of a staggered ionic potential Δ. An extensive finite-size scaling analysis is carried out on the relevant structure factors and localization operator to characterize the Mott-insulator (MI)-bond-ordered insulator (BOI)-band-insulator (BI) transitions. The intermediate BOI phase occupies a small region of the phase diagram, and this region is enlarged in the presence of Δ. In addition, the phase diagram of ionic Hubbard (the nearest-neighbor electron-electron interaction V=0) is also given.We use a density-matrix renormalization group method to study quantitatively the phase diagram of the half-filled one-dimensional (1D) extended Hubbard model in the presence of a staggered ionic potential Δ. An extensive finite-size scaling analysis is carried out on the relevant structure factors and localization operator to characterize the Mott-insulator (MI)-bond-ordered insulator (BOI)-band-insulator (BI) transitions. The intermediate BOI phase occupies a small region of the phase diagram, and this region is enlarged in the presence of Δ. In addition, the phase diagram of ionic Hubbard (the nearest-neighbor electron-electron interaction V=0) is also given.

Acta Physica SinicaJan 1, 20151 citation

Phases and Phase Transitions in the Two-Dimensional Ionic Hubbard Model

Tyler Bryant, Rajiv R. P. Singh

Bulletin of the American Physical SocietyMar 22, 20050 citations

Phase diagram of the three-dimensional Hubbard model at half filling

R. Staudt, M. Dzierzawa, A. Muramatsu

arXiv:cond-mat/0007042The European Physical Journal BOct 1, 2000120 citations

Intermediate Phase of the One Dimensional Half-Filled Hubbard-Holstein Model

Rudolf Torsten Clay, Rahul P. Hardikar

We present a numerical study of the Hubbard-Holstein model in one dimension at half filling, including finite-frequency quantum phonons. At half filling, the effects of the electron-phonon and electron-electron interactions compete with the Holstein phonon coupling acting as an effective negative Hubbard on-site interaction U that promotes on-site electron pairs and a Peierls charge-density wave state. Most previous work on this model has assumed that only Peierls or Mott phases are possible at half filling. However, there has been speculation that a third metallic phase exists between the Peierls and Mott phases. We confirm the intermediate phase, and show that the Luttinger liquid correlation exponent K(rho) >1 in this region, indicating dominant superconducting pair correlations. We explore the full phase diagram as a function of Hubbard U, phonon coupling constant, and phonon frequency.We present a numerical study of the Hubbard-Holstein model in one dimension at half filling, including finite-frequency quantum phonons. At half filling, the effects of the electron-phonon and electron-electron interactions compete with the Holstein phonon coupling acting as an effective negative Hubbard on-site interaction U that promotes on-site electron pairs and a Peierls charge-density wave state. Most previous work on this model has assumed that only Peierls or Mott phases are possible at half filling. However, there has been speculation that a third metallic phase exists between the Peierls and Mott phases. We confirm the intermediate phase, and show that the Luttinger liquid correlation exponent K(rho) >1 in this region, indicating dominant superconducting pair correlations. We explore the full phase diagram as a function of Hubbard U, phonon coupling constant, and phonon frequency.

arXiv:cond-mat/0505184Physical Review LettersAug 26, 200594 citations

U

, depending on the value of the next-nearest-neighbor hopping amplitude ${t}^{\ensuremath{'}}$, the model shows three different versions of the ground-state phase diagram. For ${t}^{\ensuremath{'}}<{t}_{c}^{{*}^{\ensuremath{'}}}$, 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 ${t}^{\ensuremath{'}}>{t}_{c}^{\ensuremath{'}}$ 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-neighbor hopping amplitude ${t}_{c}^{{*}^{\ensuremath{'}}}<{t}^{\ensuremath{'}}<{t}_{c}^{\ensuremath{'}}$ 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 to a ferroelectric insulator.