Starting from the known Lieb and Wu solution of the one-dimension-Hubbard model in the U to infinity limit, the authors show how the spin-charge decoupling of the elementary excitations is responsible for several peculiar features in one-particle properties, such as momentum distribution, quasiparticle weight and the Green function. In particular they analyse in detail the structure of the one-hole Green function at half-filling, which has not been previously calculated by field theory methods due to the breakdown of conformal invariance. A rich structure is found with branch cut singularities at omega =+or-2 sin k but no simple poles. The non-trivial dependence on the momentum of the hole allows for hole propagation although the analytic structure of G(k, omega ) is quite different from that usually characterizing band insulators. These results provide a precise characterization of one-dimensional Mott insulators. The relationship between the branch cuts of the Green function and the finite-size scaling of the quasiparticle weight is also discussed together with its implications for the analysis of numerical data.
Starting from the known Lieb and Wu solution of the one-dimension-Hubbard model in the U to infinity limit, the authors show how the spin-charge decoupling of the elementary excitations is responsible for several peculiar features in one-particle properties, such as momentum distribution, quasiparticle weight and the Green function. In particular they analyse in detail the structure of the one-hole Green function at half-filling, which has not been previously calculated by field theory methods due to the breakdown of conformal invariance. A rich structure is found with branch cut singularities at omega =+or-2 sin k but no simple poles. The non-trivial dependence on the momentum of the hole allows for hole propagation although the analytic structure of G(k, omega ) is quite different from that usually characterizing band insulators. These results provide a precise characterization of one-dimensional Mott insulators. The relationship between the branch cuts of the Green function and the finite-size scaling of the quasiparticle weight is also discussed together with its implications for the analysis of numerical data.
An exact expression for the Green's function G(k,\ensuremath{\omega}) of one hole in the U\ensuremath{\rightarrow}\ensuremath{\infty} one-dimensional Hubbard model is derived from the known Bethe-ansatz solution of the model. Due to the spin-charge decoupling of the one-hole excitation spectrum and the Fermi-like statistics of the spin excitations, G shows branch-cut singularities at \ensuremath{\omega}=\ifmmode\pm\else\textpm\fi{}2 sink and a nontrivial dependence on the momentum of the hole. As a result, the hole can propagate although the quasiparticle weight vanishes.
Using the standard Quantum Monte Carlo technique for the Hubbard model, I present here a numerical investigation of the hole propagation in a Quantum Antiferromagnet. The calculation is very well stabilized, using selected sized systems and special use of the trial wavefunction that satisfy the “close shell condition” in presence of an arbitrarily weak Zeeman magnetic field, vanishing in the thermodynamic limit. It will be shown in a forthcoming publication1 that the presence of this magnetic field does not affect thermodynamic properties for the half filled system. Then I have used the same selected sizes for the one hole ground state. I have investigated the question of vanishing or nonvanishing quasiparticle weight, in order to clarify whether the Mott insulator should behave just as conventional insulator with an upper and lower Hubbard band. By comparing the present finite size scaling with several techniques predicting a finite quasiparticle weight (see Fig.1) the data seem more consistent with a vanishing quasiparticle weight, i.e. , as recently suggested by P.W. Anderson2 the Hubbard-Mott insulator should be characterized by non-trivial excitations which cannot be interpreted in a simple quasi-particle picture. However it cannot be excluded , based only on numerical grounds, that a very small but non vanishing quasiparticle weight should survive in the thermodynamic limit.
We study a ground-state ansatz for the single-hole-doped $t\text{\ensuremath{-}}J$ model in two dimensions via a variational Monte Carlo method. Such a single-hole wave function possesses finite angular momenta generated by hidden spin currents, which give rise to a novel ground-state degeneracy in agreement with recent exact diagonalization (ED) and density matrix renormalization group (DMRG) results. We further show that the wave function can be decomposed into a quasiparticle component and an incoherent momentum distribution in excellent agreement with the DMRG results up to an $8\ifmmode\times\else\texttimes\fi{}8$ lattice. Such a two-component structure indicates the breakdown of Landau's one-to-one correspondence principle, and in particular, the quasiparticle spectral weight vanishes by a power law in the large sample size limit. By contrast, turning off the phase string induced by the hole hopping in the so-called $\ensuremath{\sigma}\ifmmode\cdot\else\textperiodcentered\fi{}t\text{\ensuremath{-}}J$ model, a conventional Bloch-wave wave function with a finite quasiparticle spectral weight can be recovered, also in agreement with the ED and DMRG results. The present study shows that a singular effect already takes place in the single-hole-doped Mott insulator, by which the bare hole is turned into a non-Landau quasiparticle with translational-symmetry breaking. Generalizations to pairing and finite doping are briefly discussed.
The author calculates an exact expression for the Green function of a single hole in a Neel background, for finite Ising interaction J z identical to 4t 2 /U where t is the hopping (overlap) integral in the Hubbard model and U the usual on-site interaction. In 1D for fixed boundary conditions, loops are absent and thus the expression is exact and independent of the retraceable path approximation, while in 2D the expression is exact to within the exclusion of loops. The spectral function A( omega ) shows delta-function peaks at well defined energy spacings, with damping only at frequencies omega >5/2J z different from earlier results. These peaks are necessary for the existence of quasiparticles. The author presents an argument that, for sufficiently large U, the discrete spectrum in A( omega ) merges to a continuous 'band' as the weight varies as J z of the poles vanishes in the U= infinity limit and hence that use of the latter does not necessarily imply incoherent behaviour in the system.
Holes in a Mott insulator are represented by spinless fermions in the fermion-boson model introduced by Edwards. Although the physically interesting regime is for low to moderate fermion density, the model has interesting properties over the whole density range. It has previously been studied at half-filling in the one-dimensional (1D) case by numerical methods, in particular using exact diagonalization and the density matrix renormalization group (DMRG). In the present study the one-particle Green's function is calculated analytically by means of a decoupling scheme for the equations of motion, valid for arbitrary density in 1D, 2D and 3D with fairly large boson energy and zero boson relaxation parameter. The Green's function is used to compute some ground state properties, and the one-fermion spectral function, for fermion densities n = 0.1, 0.5 and 0.9 in the 1D case. The results are generally in good agreement with numerical results obtained using the DMRG and dynamical DMRG, and new light is shed on the nature of the ground state at different fillings. The Green's function approximation is sufficiently successful in 1D to justify future application to the 2D and 3D cases.
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.