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arXiv:cond-mat/0607568 · Physical Review Letters

Correlated Insulated Phase Suggests Bond Order between Band and Mott Insulators in Two Dimensions

S. S. Kancharla, Elbio R. Dagotto

Published Jan 5, 2007• 91 citations
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Abstract

We investigate the ground state phase diagram of the half-filled repulsive Hubbard model in two dimensions in the presence of a staggered potential Delta, the so-called ionic Hubbard model, using cluster dynamical mean-field theory. We find that for large Coulomb repulsion, U >> Delta, the system is a Mott insulator (MI). For weak to intermediate values of Delta, on decreasing U, the Mott gap closes at a critical value Uc1(Delta) beyond which a correlated insulating phase with possible bond order is found. Further, this phase undergoes a first-order transition to a band insulator (BI) at Uc2(Delta) with a finite charge gap at the transition. For large Delta, there is a direct first-order transition from a MI to a BI with a single metallic point at the phase boundary.

DOI
10.1103/physrevlett.98.016402

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The ground-state phase diagram of the half-filled repulsive Hubbard model in a bilayer is investigated using cluster dynamical mean-field theory. For weak to intermediate values of Coulomb repulsion UUU, the system undergoes a transition from a Mott-insulating phase to a metallic phase and then onto a band-insulating phase as the interlayer hopping is increased. In the strong-coupling case, the model exhibits a direct crossover from a Mott-insulating phase to a band-insulating phase. These results are robust with respect to the presence or absence of magnetic order.
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 UUU, 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<UcU<{U}_{c}U<Uc​, ferroelectric insulator at Uc<U<Us{U}_{c}<U<{U}_{s}Uc​<U<Us​, and correlated (Mott) insulator at U>UcU>{U}_{c}U>Uc​. For ${t}^{\ensuremath{'}}>{t}_{c}^{\ensuremath{'}}$ there is only one transition from a spin-gapped metallic phase at U<UcU<{U}_{c}U<Uc​ to a ferroelectric insulator at U>UcU>{U}_{c}U>Uc​. 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 Uc1{U}_{c1}Uc1​ the model undergoes a second-order commensurate-incommensurate-type transition from a band insulator into a metallic state and at larger Uc2{U}_{c2}Uc2​ there is a Kosterlitz-Thouless-type transition from a metal to a ferroelectric insulator.
We investigate the quantum phase transitions in the half-filled ionic Hubbard model on a two-dimensional (2D) square lattice using the variational cluster approach (VCA). We present explicit evidence for the tendency toward a novel intermediate phase in this model. This phase is characterized by bond-located magnetization. For weak Coulomb repulsion U , the system is a band insulator, and then undergoes a transition to the intermediate phase at the first-phase boundary U = U c1 . As U is increased beyond the second transition point U c2 , there occurs a Mott insulator accompanied by a long-range antiferromagnetic (AF) order. The bond-located spin density wave competes with the antiferromagnetism while the charge-density modulation exists all the way due to the staggered potential Δ.
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 investigate the ground-state phase diagram of the one-dimensional 'ionic' Hubbard model with an alternating periodic potential at half-filling by numerical diagonalization of finite systems with the Lanczos and density matrix renormalization group methods. We identify an insulator–insulator phase transition from a band to a correlated insulator with simultaneous charge and bond-charge order. The transition point is characterized by the vanishing of the optical excitation gap while simultaneously the charge and spin gaps remain finite and equal. Indications for a possible second transition into a Mott-insulator phase are discussed.
A detailed study of electronic phase transitions in the ionic Hubbard model at half filling is presented. Within the dynamical mean field approximation a series of transitions from the band insulator via a metallic state to a Mott--Hubbard insulating phase is found at intermediate values of the one-body potential $\ensuremath{\Delta}$ with increasing the Coulomb interaction UUU. We obtain a critical region in which the metallic phase disappears and a coexistence phase between the band and the Mott insulating state sets in. Our results are consistent with those obtained at low dimensions, thus they provide a concrete description for the charge degrees of freedom of the ionic Hubbard model.