The single particle spectral-weight function (SWF) of the ionic Hubbard model at half filling is calculated in the cluster perturbation theory approximation. An abrupt change of regime in the low-energy region, near the chemical potential, is found at a critical value, $U_{c}$, of the coupling constant (Hubbard $U$). The SWF at the Fermi points $k_{F}$=$\pmπ/2$ jumps, as $U$ increases, from a two-peak structure, the gap edges, to a four-peak structure accompanied by a (non-vanishing) minimum of the charge-gap. The two inner peaks of this structure show very small dispersion (flat bands) away from the Fermi points, whereas the outer peaks mark the edges of the Hubbard bands. No other signatures of abrupt change are detected in the SWF. The two regimes are physically realized in the angle-resolved photoelectron spectra of $(TaSe_{4})_{2}I$, and the blue-bronze $K_{0.3}MoO_{3}$, respectively.
The single particle spectral-weight function (SWF) of the ionic Hubbard model at half filling is calculated in the cluster perturbation theory approximation. An abrupt change of regime in the low-energy region, near the chemical potential, is found at a critical value, Uc, of the coupling constant (Hubbard U). The SWF at the Fermi points kF=±π/2 jumps, as U increases, from a two-peak structure, the gap edges, to a four-peak structure accompanied by a (non-vanishing) minimum of the charge-gap. The two inner peaks of this structure show very small dispersion (flat bands) away from the Fermi points, whereas the outer peaks mark the edges of the Hubbard bands. No other signatures of abrupt change are detected in the SWF. The two regimes are physically realized in the angle-resolved photoelectron spectra of (TaSe4)2I, and the blue-bronze K0.3MoO3, respectively.
We show in this paper that the single-particle spectral-weight function (SWF) of the one-dimensional ionic Hubbard model at half filling exhibits critical behavior, as a function of the on-site repulsion U, near the chemical potential. The calculation has been carried out within the framework of the cluster perturbation theory approach of Senechal et al., Phys. Rev. Lett 84, 522 (2000). As U increases, the SWF at ${k}_{F}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}∕2$ (the Fermi points) jumps from the two-peak structure (plus two weak side peaks) characteristic of low U<Uc to a four-peak structure beyond Uc where all the peaks have about the same spectral weight. This abrupt spectral-weight transfer from the inner to the outer peaks can be traced to the ionic-neutral transition characteristic of this system and seems to correspond to the first critical point of the two-point scenario discussed in the literature. It is accompanied by a nonvanishing minimum of the single-particle charge gap. As U increases further, the system evolves gradually into a Mott-Hubbard insulator. No other signatures of abrupt change are detected in the SWF. These results are discussed in the light of photoelectron spectroscopic measurements of quasi-one-dimensional materials.
The one-electron spectral-weight function of the half-filled ionic Hubbard model is calculated by means of Quantum Monte Carlo. A metallic regimen occurs between two values of the coupling constant (Hubbard U) U1 < U2 . The system is a band insulator below U1, and an increasingly antiferromagnetic (AF) insulator above U2 evolving into a Mott insulator as U tends to infinity . The intermediate regimen which is both AF and dimerized, is caused by a two-peak structure at k = 0,5 pi (the Fermi surface). As U increases both peaks approach each other, overlap, and separate again, the system becoming metallic in the overlap region.
An analytic approach is presented of electronic one-particle spectra of the one-band Hubbard model at half filling in the antiferromagnetic phase. Starting from the strong-coupling regime U\ensuremath{\gg}:t, a projection technique is used to set up self-consistent coupled equations for the electron Green function, which are valid down to values U\ensuremath{\approx}t. The self-consistent equation for the hole propagator is a direct generalization of the one found from the t-J model. This gives further support to the ``string'' picture, where propagation of holes creates strings of overturned spins with which the holes interact. In the present work hopping of holes (or electrons) with up spin on the down sublattice is also taken into acount, as well as transitions between the lower and upper Hubbard bands. These are shown to change significantly the incoherent part of the t-J model spectra, by smearing out the shake-off peaks, reminiscent of higher bound string states due to multispin scattering. Coherent (quasiparticle) peaks exist at the band edges, on both sides of the insulating gap. We show that with decreasing U the quasiparticle concept loses its meaning for wave vectors at the center of the magnetic Brillouin zone (MBZ). For large values of U the dispersion of the quasiparticle is found to scale with its band width, which is of order J. Extrema are always found at k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2). The weight of the quasiparticle at this k value decreases logarithmically with increasing U. In the strong-coupling limit the spectrum tends to be symmetric, i.e., to become an even function of the frequency around the chemical potential, for any wave vector. For small values of U the dispersion at the edge of the MBZ flattens away, as expected when approaching the noninteracting limit. The spectral function in this regime, for wave vectors away from the edge of the MBZ, is concentrated mainly on one side of the chemical potential.
We calculate the single-particle Green's function for the tight-binding band structure, ξp=−2tcospx−2tcospy−μ, with a function of chemical potential μ for square-lattice system. The form of the single-particle self-energy, Σ(p,E), is determined by the density-density correlation function, χ(q,ω), which develops two peaks for μ≳−2.5t unlike parabolic band case. Near half filling χ(q,ω) becomes independent of ω, one dimensional behavior, at intermediate values of ω which leads to one dimensional behavior in Σ(p,E). However μ≤−0.1t there is no influence on the Fermi Liquid dependences from SDW instability. The strong p and E dependence of the off-shell self-energy, Σ(p,E), found earlier for the parabolic band is recovered for μ≲−t but deviations from this develop for μ≳−0.1t. The resonance peak width of the spectral function, A(p,E) has linear dependence in ξp due to the E dependence of the imaginary part of Σ(p,E). We point out that an accurate detailed form for Σ(p,E) would be very difficult to recover from ARPES data for the spectral density.
Implementing an improved method for analytic continuation and working with imaginary-time correlation functions computed using quantum Monte Carlo simulations, we resolve the single-particle dispersion relation and the density of states (DOS) of the two-dimensional Hubbard model at half filling. At intermediate interactions of U/t=4,6, we find quadratic dispersion around the gap minimum at wave vectors $\mathbf{k}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2)$ (the $\mathrm{\ensuremath{\Sigma}}$ points). We find saddle points at $\mathbf{k}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0),(0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi})$ (the X points), where the dispersion is approximately quartic, leading to a sharp DOS maximum above the almost flat ledge arising from the states close to $\mathrm{\ensuremath{\Sigma}}$. The fraction of quasiparticle states within the ledge is ${n}_{\mathrm{ledge}}\ensuremath{\approx}0.15$. Upon doping away from half filling, within the rigid-band approximation, these results support Fermi pockets around the $\mathrm{\ensuremath{\Sigma}}$ points, with states around the X points becoming filled only at doping fractions $x\ensuremath{\ge}{n}_{\mathrm{ledge}}$. The high density of states away from the $\mathrm{\ensuremath{\Sigma}}$ gap edge may be an important clue for a finite minimum doping level for superconductivity and other instabilities of doped Mott insulators.
Thermodynamic and dynamical properties of filling-control metal-insulator transition (MIT) in the Hubbard model are studied by the operator projection method, especially in two dimensions. This is a non-perturbative analytic approach to many-body systems. The present theory incorporates the Mott-Hubbard, Brinkman-Rice and Slater pictures of the MIT into a unified framework, together with reproducing low-energy narrow band arising from spin-charge fluctuations. At half filling, single-particle spectra A(ω,k) show formation of two Hubbard bands and their antiferromagnetic shadows separated by a Mott gap in the plane of energy ω and momentum k with lowering temperatures. These four bands produce splitting to two low-energy narrow bands and two SDW-like bands in the dispersion. Near half filling, the low-energy narrow band persists at low temperatures. This narrow band has a particularly weak dispersion and large weights around (π,0) and (0,π) momenta. The velocity of these low-energy excitations is shown to vanish towards the MIT, indicating the mass divergence as in the Brinkman-Rice picture, but most prominently around (π,0) and (0,π) with strong momentum dependence. This reflects the suppression of the coherence near the MIT. Main structures in A(ω,k) show remarkable similarities to quantum Monte-Carlo results in two dimensions as well as in the one-dimensional Hubbard model. The charge compressibility appears to diverge with decreasing doping concentration in both one and two dimensions in agreement with the exact and quantum Monte-Carlo results. We also discuss implications of the flat dispersion formed near the Fermi level to the observations in high-$\Tc$ cuprate superconductors.