The momentum dispersion of the peak structure of the single-particle spectral weight A(p,\ensuremath{\omega}) of the two-dimensional Hubbard model is discussed. Using results obtained from Monte Carlo simulations on lattices up to 12\ifmmode\times\else\texttimes\fi{}12 in size, we determine the low-lying quasiparticle dispersion relation. This dispersion relation is anomalously flat near the (\ensuremath{\pi},0) and (0,\ensuremath{\pi}) points of the Brillouin zone, similar to the results of recent angular resolved photoemission measurements of the hole-doped cuprates. We argue that the generic nature of the quasiparticle dispersion relation observed in these materials arises from the strong Coulomb interaction and reflects the hole-spin correlations rather than the one-electron interactions which customarily determine the band structure.
The Hubbard model at half-filling is a collective, antiferromagnetic insulator. We study added electrons or holes. The insulating energy gap and the dispersion of the added carriers are calculated variationally in two dimensions with use of a Monte Carlo evaluation of the electronic correlation functions in the insulating phase. Both
Eg and
m∗ are found to be temperature dependent.
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.
We show numerically that the nature of the doping-induced metal-insulator transition in the two-dimensional Hubbard model with hopping matrix element
t and Coulomb repulsion
U is radically altered by the inclusion of a term
W that depends upon a square of a single-particle nearest-neighbor hopping. This result is reached by computing the localization length ${\ensuremath{\xi}}_{l}$ in the insulating state. At
W/t=0.05 and
U/t=4, we find results consistent with ${\ensuremath{\xi}}_{l}\ensuremath{\sim}|\ensuremath{\mu}\ensuremath{-}{\ensuremath{\mu}}_{c}{|}^{\ensuremath{-}1/2}$ where ${\ensuremath{\mu}}_{c}$ is the critical chemical potential. In contrast, ${\ensuremath{\xi}}_{l}\ensuremath{\sim}|\ensuremath{\mu}\ensuremath{-}{\ensuremath{\mu}}_{c}{|}^{\ensuremath{-}1/4}$ for the Hubbard model at
U/t=4. At half-filling, we calculate the density of states $N(\ensuremath{\omega})$. The large value of $N(\ensuremath{\omega})$ in the vicinity of $\ensuremath{\omega}={\ensuremath{\mu}}_{c}$ present at
W=0 is suppressed with growing values of
W. At finite doping, the
d-wave pair-field correlations are enhanced with growing values of
W. The numerical results imply that at finite values of
W doping the antiferromagnetic Mott insulator leads to a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductor.
For the
t-
J model, variational wave functions can generally be constructed based on an accurate description of antiferromagnetism (AFM) at half-filling and an exact phase-string sign structure under doping. The single-hole-doped and two-hole-doped states, as determined by variational Monte Carlo (VMC) simulations, display sharply contrasting behaviors. The single-hole state constitutes a ``cat state'' that resonates strongly between a quasiparticle component and a local loop-current component, with approximately equal weights. In the ground state, the quasiparticle spectral weight
Zk peaks at momenta
k0≡(±2π,±2π). The total-energy dispersion versus
k agrees remarkably well with the Green function Monte Carlo results. However, Landau's one-to-one correspondence hypothesis for quasiparticles breaks down here with the incoherent component exhibiting intrinsic magnetization originating from a minimal
2×2 loop current that forms a
4×4 pattern on the square lattice--a finding in excellent agreement with density matrix renormalization group (DMRG) calculations. In the two-hole ground state, a new pairing mechanism is revealed: the two holes are automatically fused into a tightly bound object consisting of an incoherent
dxy pairing along the diagonal direction by compensating the local loop currents. This hole pair is again a ``cat state'' that resonates strongly between the incoherent
dxy and a coherent
dx2−y2 Cooper channel to gain substantial hopping energy. Its size extends over an area of about
4×4 lattice spacings, much smaller than the divergent AFM correlation length, implying that it should survive as a minimal superconducting building block even in the dilute doping regime. Experimental implications and the generalization to the finite-doping case are briefly addressed.
We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods established the stripe order as the ground state near
1/8 doping at strong interactions. In this paper, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo (AFQMC) method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about
1/5 doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes.