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Modern Physics Letters B

PHASE TRANSITION IN THE HALF-FILLED IONIC HUBBARD MODEL: MEAN-FIELD SLAVE BOSON STUDY

Duc‐Anh Le, Anh-Tuan Hoang

Published Dec 19, 2011• 2 citations
Publisher

Abstract

We study electronic phase transitions in the half-filled ionic Hubbard model with an on-site Coulomb repulsion U and an ionic energy Δ by using the Kotliar–Ruckenstein slave-boson theory. Assuming a paramagnetic solution, we show that for any non-zero values of Δ, with increasing U the system undergoes a transition from band-insulator to Mott-insulator. Our results have implied the absence of a metallic phase between the band and the Mott insulator phases.

DOI
10.1142/s0217984911500163

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We study electronic phase transitions in the half-filled ionic Hubbard model with an on-site Coulomb repulsion U and an ionic energy Δ by using the Kotliar–Ruckenstein slave-boson theory. Assuming a paramagnetic solution, we show that for any non-zero values of Δ, with increasing U the system undergoes a transition from band-insulator to Mott-insulator. Our results have implied the absence of a metallic phase between the band and the Mott insulator phases.
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.
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 metal-insulator transition in the half-filled Hubbard model on the two-dimensional triangular lattice using both the Kotliar-Ruckenstein slave-boson technique and an exact numerical diagonalization of finite clusters. Contrary to the case of a square lattice, where a perfect nesting of the Fermi surface leads to a metal-insulator transition at arbitrarily small values of U, always accompanied by antiferromagnetic ordering, on a triangular lattice, due to the lack of perfect nesting, the transition takes place at a finite value of U, and frustration induces a nontrivial competition among different magnetic phases. Indeed, within the mean-field approximation in the slave-boson approach, as the interaction grows the paramagnetic metal turns into a metallic phase with incommensurate spiral ordering. Increasing the interaction further, a linear spin-density wave is stabilized, and finally for strong coupling the latter phase undergoes a first-order transition toward an antiferromagnetic insulator. No trace of the intermediate phases is seen in the exact diagonalization results, indicating a transition between a paramagnetic metal and an antiferromagnetic 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 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 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.
The Mott - Hubbard metal - insulator transition in the half-filled mass imbalanced ionic Hubbard model is investigated using the two-site dynamical mean field theory. We find that for a fixed mass imbalanced parameter r the critical interaction Uc increases when the ionic energy Δ\DeltaΔ is increased. In the other hand, for a fixed Δ\DeltaΔ, UcU_cUc​ decreases with increasing the mass imbalance. We also show the existence of BI phase in the system for the case Δ≠0\Delta \ne 0Δ=0, U=0U=0U=0 and calculate the staggered charge density nB−nAn_B − n_AnB​−nA​ as a function of the interaction for different values of the mass imbalance. Our results in the limiting cases (r=1r = 1r=1; Δ≠0\Delta \ne 0Δ=0 or/and Δ=0\Delta = 0Δ=0; r≠1r\ne 1r=1) are in good agreement with those obtained from full dynamical mean field theory.