Ionic Hubbard Model Research Articles

Exploring competing density order in the ionic Hubbard model with ultracold fermions.

We realize and study the ionic Hubbard model using an interacting two-component gas of fermionic atoms loaded into an optical lattice. The bipartite lattice has a honeycomb geometry with a staggered energy offset that explicitly breaks the inversion symmetry. Distinct density-ordered phases are identified using noise correlation measurements of the atomic momentum distribution. For weak interactions the geometry induces a charge density wave. For strong repulsive interactions we detect a strong suppression of doubly occupied sites, as expected for a Mott insulating state, and the externally broken inversion symmetry is not visible anymore in the density distribution. The local density distributions in different configurations are characterized by measuring the number of doubly occupied lattice sites as a function of interaction and energy offset. We further probe the excitations of the system using direction dependent modulation spectroscopy and discover a complex spectrum, which we compare with a theoretical model.

Phase diagram of the half-filled ionic Hubbard model

We study the phase diagram of the ionic Hubbard model (IHM) at half-filling using dynamical mean field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered potential $\Delta$ and the on-site Hubbard U. In both the methods we find that for a finite $\Delta$ and at zero temperature, anti-ferromagnetic (AFM) order sets in beyond a threshold $U=U_{AF}$ via a first order phase transition below which the system is a paramagnetic band insulator. Both the methods show a clear evidence for a transition to a half-metal phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U. We show that the results obtained within both the methods have good qualitative and quantitative consistency in the intermediate to strong coupling regime. On increasing the temperature, the AFM order is lost via a first order phase transition at a transition temperature $T_{AF}(U, \Delta)$ within both the methods, for weak to intermediate values of U/t. But in the strongly correlated regime, where the effective low energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. As a result, at any finite temperature T, DMFT+CTQMC shows a second phase transition (not seen within DMFT+IPT) on increasing U beyond $U_{AF}$. At $U_N > U_{AF}$, when the Neel temperature $T_N$ for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second order transition. In the 3-dimensonal parameter space of $(U/t,T/t,\Delta/t)$, there is a line of tricritical points that separates the surfaces of first and second order phase transitions.

Phase transitions of the ionic Hubbard model on the honeycomb lattice.

Many-body problem on the honeycomb lattice systems have been the subject of considerable experimental and theoretical interest. Here we investigate the phase transitions of the ionic Hubbard model on the honeycomb lattice with an alternate ionic potential for the half filling and hole doping cases by means of cellular dynamical mean field theory combining with continue time quantum Monte Carlo as an impurity solver. At half filling, as the increase of the interaction at a fixed ionic potential, we find the single particle gap decreases firstly, reaches a minimum at a critical interaction , then increases upturn. At , there is a band insulator to Mott insulator transition accompanying with the presence of the antiferromagnetic order. Away from half filing, the system shows three phases for the different values of hole density and interaction, paramagnetic metal, antiferromagnetic metal and ferromagnetic metal. Further, we present the staggered particle number, the double occupancy, the staggered magnetization, the uniform magnetization and the single particle spectral properties, which exhibit characteristic features for those phases.

From gapped excitons to gapless triplons in one dimension

Often, exotic phases appear in the phase diagrams between conventional phases. Their elementary excitations are of particular interest. Here, we consider the example of the ionic Hubbard model in one dimension. This model is a band insulator (BI) for weak interaction and a Mott insulator (MI) for strong interaction. Inbetween, a spontaneously dimerized insulator (SDI) occurs which is governed by energetically low-lying charge and spin degrees of freedom. Applying a systematically controlled version of the continuous unitary transformations (CUTs) we are able to determine the dispersions of the elementary charge and spin excitations and of their most relevant bound states on equal footing. The key idea is to start from an externally dimerized system using the relative weak interdimer coupling as small expansion parameter which finally is set to unity to recover the original model.

Effects of correlations on honeycomb lattice in ionic-Hubbard model

In a honeycomb lattice the symmetry has been broken by adding an ionic potential and a single-particle gap was generated in the spectrum. We have employed the iterative perturbation theory (IPT) in dynamical mean field approximation method to study the effects of competition between $U$ and $\Delta$ on energy gap and renormalized Fermi velocity. We found, the competition between the single-particle gap parameter and the Hubbard potential closed the energy gap and restored the semi-metal phase, then the gap is opened again in Mott insulator phase. For a fixed $\Delta$ by increasing $U$, the renormalized Fermi velocity $\tilde{v_F}$ is decreased, but change in $\Delta$, for a fixed $U$, has no effects on $\tilde{v_F}$. The difference in filling factor is calculated for various number of $U, ~\Delta$. The results of this study can be implicated for gapped graphene e.g. hydrogenated graphene.

Phase diagram of the one-dimensional extended ionic Hubbard model

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.

Conductivity in Half-filled Ionic Hubbard Model

We calculate the temperature dependent conductivity in the half-filled ionic Hubbard model with an on-site Coulomb repulsion $U$ and an ionic energy $\Delta$ by mean of the coherent potential approximation. It is shown that for intermediate and large \(\Delta\) the largest conductivity occurs near the special value \(U = 2 \Delta\) at all temperatures \(T\), for a fixed \(\Delta\) the region of finite conductivity \([U_{c1}, U_{c2}]\) expands and its maximum decreases with increasing \(T\). Our results are in good agreement with those derived from the determinant quantum Monte Carlo simulation.

Dispersive excitations in one-dimensional ionic Hubbard model

A detailed study of the one-dimensional ionic Hubbard model with interaction $U$ is presented. We focus on the band insulating (BI) phase and the spontaneously dimerized insulating (SDI) phase which appears on increasing $U$. By a recently introduced continuous unitary transformation [H. Krull et al., Phys. Rev. B 86, 125113 (2012)] we are able to describe the system even close to the phase transition from BI to SDI although the bare perturbative series diverges before the transition is reached. First, the dispersion of single fermionic quasiparticles is determined in the full Brillouin zone. Second, we describe the binding phenomena between two fermionic quasiparticles leading to an $S=0$ and to an $S=1$ exciton. The latter corresponds to the lowest spin excitation and defines the spin gap which remains finite through the transition from BI to SDI. The former becomes soft at the transition, indicating that the SDI corresponds to a condensate of these $S=0$ excitons. This view is confirmed by a BCS mean-field theory for the SDI phase.

Inclusion of intersite spatial correlations in the alloy analogy approach to the half-filled ionic Hubbard model

Using the nonlocal coherent-potential approximation we study the effect of intersite spatial correlations on the transition from band insulator to metal as well as from metal to Mott insulator in the ‘alloy analogy’ approach to the paramagnetic solution of the half-filled ionic Hubbard model. We find that intersite spatial correlations enhance the metallic phase.

Physics of metal-corrrelated barrier with chemical modulation-metal heterostructure

Barrier planes described by the Ionic Hubbard model sandwiched between metallic planes on both sides are studied using unrestricted Hartree Fock. For zero onsite correlation, the presence of the metallic interface generates an additional gap in the energy spectrum away from half filling, if the chemically modulated potential in the barrier planes exceed a critical value. There is an insulator–metal–insulator transition as we tune onsite correlation for fixed strength of chemical modulation. The metallic behaviour penetrates the barrier planes due to proximity effect. The variation of the gaps for varying numbers of intermediate planes is also determined.

Finite-temperature phase transitions in the ionic Hubbard model

We investigate paramagnetic metal-insulator transitions in the infinite-dimensional ionic Hubbard model at finite temperatures. By means of the dynamical mean-field theory with an impurity solver of the continuous-time quantum Monte Carlo method, we show that an increase in the interaction strength brings about a crossover from a band insulating phase to a metallic one, followed by a first-order transition to a Mott insulating phase. The first-order transition turns into a crossover above a certain critical temperature, which becomes higher as the staggered lattice potential is increased. Further, analysis of the temperature dependence of the energy density discloses that the intermediate metallic phase is a Fermi liquid. It is also found that the metallic phase is stable against strong staggered potentials even at very low temperatures.

Ferromagnetic response of a “high-temperature” quantum antiferromagnet

We study the finite temperature antiferromagnetic phase of the ionic Hubbard model in the strongly interacting limit using quantum Monte Carlo based dynamical mean field theory. We find that the ionic potential plays a dual role in determining the antiferromagnetic order. A small ionic potential (compared to Hubbard repulsion) increases the super-exchange coupling in the projected sector of the model, leading to an increase in the Neel temperature of the system. A large ionic potential leads to resonance between projected antiferromagnetically ordered configurations and density ordered configurations with double occupancies, thereby killing antiferromagnetism in the system. This novel way of degrading antiferromagnetism leads to spin polarization of the low energy single particle density of states. The dynamic response of the system thus mimics ferromagnetic behaviour, although the system is still an antiferromagnet in terms of the static spin order.

Disappearance of the Dirac cone in silicene due to the presence of an electric field

Using the two-dimensional ionic Hubbard model as a simple basis for describing the electronic structure of silicene in the presence of an electric field induced by the substrate, we use the coherent-potential approximation to calculate the zero-temperature phase diagram and the associated spectral function at half filling. We find that any degree of symmetry-breaking induced by the electric field causes the silicene structure to lose its Dirac fermion characteristics, thus providing a simple mechanism for the disappearance of the Dirac cone.

Electric polarization in correlated insulators

We derive a formula for the electric polarization of interacting insulators, expressed in terms of the full Green's and vertex functions. We exemplify this method in the half-filled ionic Hubbard model treated within dynamical mean field theory (DMFT). The electric polarization of a correlated band insulator is determined by the interplay of ionicity and covalency, and both quantities are renormalized by the electron-electron interactions. We introduce quasiparticle approximation to the exact equation for the polarization, and compare the results of this approximation with those of the exact DMFT formulation and of static mean field theories such as the LDA+ U. The latter overestimates the electronic contribution to the electric polarization when the quasiparticle weight of the active bands is very small.

Exact exchange-correlation potential of an ionic Hubbard model with a free surface

In Kohn-Sham density functional theory (DFT) the interacting electron problem is mapped into a noninteracting problem in an effective potential vKS. It is known that the charge gap of the interacting system is different from the gap of the effective problem due to a jump Δxc in vKS when an electron is added but its magnitude and its role in the ubiquitous discrepancy between the experimental gaps and approximate DFT computations is poorly understood. Here we compute the exact vKS of a strongly interacting one-dimensional lattice model which can be driven from an ionic to a Mott insulating state. Presence of a “vacuum” region allows to determine the absolute value of vKS. We show that in the ionic regime Δxc is determined by nearest-neighbor interaction, while in the Mott regime Δxc is determined by on-site Hubbard interaction.

Magnetic transition in a correlated band insulator

The effect of on-site electron-electron repulsion $U$ in a band insulator is explored for a bilayer Hubbard Hamiltonian with opposite sign hopping in the two sheets. The ground state phase diagram is determined at half-filling in the plane of $U$ and the interplanar hybridization $V$ through a computation of the antiferromagnetic (AF) structure factor, local moments, single particle and spin wave spectra, and spin correlations. Unlike the case of the ionic Hubbard model, no evidence is found for a metallic phase intervening between the Mott and band insulators. Instead, upon increase of $U$ at large $V$, the behavior of the local moments and of single-particle spectra give quantitative evidence of a crossover to a Mott insulator state preceding the onset of magnetic order. Our conclusions generalize those of single-site dynamical mean field theory, and show that including interlayer correlations results in an increase of the single particle gap with $U$.

Band and Mott Insulators and Superconductivity in Honeycomb-Lattice Ionic-Hubbard Model

Motivated by superconductivity (SC) in layered nitrides, we study an ionic-Hubbard model of a honeycomb lattice, which consists of two sublattices with an energy-level offset, by an optimization variational Monte Carlo method. The parameters for the Coulomb interaction and energy-level offset to realize a band insulator in the nondoped state are evaluated, and the SC state is investigated in a carrier-doped band insulator. It is found that, in a weakly doped band insulator, spin fluctuation remains and the spin-singlet \(d\)-wave SC state is realized. Present results support an unconventional spin-singlet SC state suggested by the experimental observations in layered nitrides.

Superconductivity in ionic-Hubbard model on honeycomb lattice

To consider the origin of superconductivity (SC) in layered nitride superconductors, we study an ionic-Hubbard model on a honeycomb lattice, which consists of two sublattices with a level offset, using an optimization variational Monte Carlo method. The parameter values for the Coulomb interaction and the level offset, to realize a band insulator, is evaluated in the non-doped system. In carrier-doped band insulating systems, a spin singlet d-wave SC state is stabilized. The spin fluctuation remains relatively strong even for large level offsets. We find that a renormalization effect of the energy band primarily contributes to the spin fluctuation.

Quantum Monte Carlo study on an ionic Hubbard model in one dimension

We study an ionic Hubbard model in one dimension by using a quantum Monte Carlo method. The ionic Hubbard model we study is a strongly correlated model for electrons in alternating potentials with a lattice period of 2. By modifying the Hirsch-Fye algorithm, we incorporate the local variation of the potential in the weight of the partition function at each imaginary-time segment. For a given alternating potential of strength Δ = 1.0, as we change the local Coulomb repulsion, U, between spin-up and spin-down electrons, we calculate various physical quantities, including kinetic energies, correlation energies, and band energies. We try to find the signature of the phase transitions from the behavior of the kinetic energy and that of double occupancies at finite temperatures.

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

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.