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Physical review. B, Condensed matter

Electron-momentum distribution function and spectral function in thet-Jmodel

R. Eder, K. W. Becker

Published Oct 1, 1991• 29 citations
Publisher

Abstract

The momentum distribution function and electron spectral function for mobile holes in an antiferromagnet as described by the t-J model are discussed. The calculations are done using a trial wave function for the coherent motion of an individual hole based on a string picture. To discuss finite concentrations, the rigid-band approximation is assumed to be valid. Despite this both quantities considered are qualitatively similar to what one would expect for weakly interacting particles occupying the tight-binding band calculated from the hopping term in the Hamiltonian.

DOI
10.1103/physrevb.44.6982

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Hubbard one-particle Green function in the antiferromagnetic phase

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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.

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Spatial distribution of mobile holes in thet-Jmodel

K. J. E. Vos, Robert J Gooding, P. W. Leung +1 more

We have calculated the hole-hole correlation function for two holes doped into a S=1/2 antiferromagnetic insulator described by the t-J model on a 16-site \ensuremath{\surd}8\ifmmode\times\else\texttimes\fi{}\ensuremath{\surd}32 lattice and a 24-site \ensuremath{\surd}18\ifmmode\times\else\texttimes\fi{}\ensuremath{\surd}32 lattice using an exact diagonalization technique. We predict that the carriers described by this model, in the parameter range relevant to ${\mathrm{CuO}}_{2}$ planes, tend to stay as far apart as possible. This result is in direct contradiction to previously published exact diagonalization data [e.g., D. Poilblanc, Phys. Rev. B 49, 1477 (1994)]. We suggest that if the carriers do tend to stay as far apart from one another as possible, then the electron momentum distribution function shows evidence for hole pockets at k\ensuremath{\rightarrow}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), consistent with many recent studies of these models, including recent photoemission work.

Physical review. B, Condensed matter•May 1, 1995•0 citations
The momentum distribution function and electron spectral function for mobile holes in an antiferromagnet as described by the t-J model are discussed. The calculations are done using a trial wave function for the coherent motion of an individual hole based on a string picture. To discuss finite concentrations, the rigid-band approximation is assumed to be valid. Despite this both quantities considered are qualitatively similar to what one would expect for weakly interacting particles occupying the tight-binding band calculated from the hopping term in the Hamiltonian.
We calculated the momentum distribution and one-particle spectral function for the ground state of two holes in a finite-cluster t-J model in the framework of the string picture. Previous numerical results for these quantities could be reproduced at least qualitatively. Our interpretation of these data, however, supports a rigid-band approximation starting from the single-hole case rather than a nearest-neighbor hopping band and large Fermi surface. We argue that in order to interpret the finite-cluster data properly, it is crucial to take into account the well-established fact that the ground state of two holes in a finite cluster is a bound state with nontrivial symmetry.
We examine the effects of electron-phonon interaction on the dynamics of the charge carriers doped in two-dimensional (2D) Heisenberg antiferromagnet. The t-J model Hamiltonian with a Fr\"ohlich term which couples the holes to a dispersionless (optical) phonon mode is considered for low doping concentration. The evolution of the spectral density function, the density of states, and the momentum distribution function of the holes with an increase of the hole-phonon coupling constant g is studied numerically. As the coupling to a phonon mode increases the quasiparticle spectral weight decreases and a ``phonon satellite'' feature close to the quasiparticle peak becomes more pronounced. Furthermore, strong electron-phonon coupling smears the multimagnon resonances (``string states'') in the incoherent part of the spectral function. The jump in the momentum distribution function at the Fermi surface is reduced without changing the hole pocket volume, thereby providing a numerical verification of Luttinger theorem for this strongly interacting system. The vertex corrections due to electron-phonon interaction are negligible in spite of the fact that the ratio of the phonon frequency to the effective bandwidth is not small. \textcopyright{} 1996 The American Physical Society.
We present a nonperturbative method for deriving a quasiparticle description of the low-energy excitations in the t-J model for strongly correlated electrons. Using the exact diagonalization technique we evaluated exactly the spectral functions of composite operators, which describe an electron or hole dressed by antiferromagnetic spin fluctuations as expected in the string or spin bag picture. For hole doping up to 1/8, use of the composite operators leads to a drastic simplification of the single-particle spectral function: at half-filling it takes free-particle form, for the doped case it resembles a system of weakly interacting fermions corresponding to the doped holes. We conclude that for all doping levels studied, the elementary electronic excitations next to the Fermi level are adequately described by the antiferromagnetic spin-fluctuation picture.
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.
Abstract The dynamics of a hole motion in a quantum antiferromagnet has been studied in the past three decades because of its relationship to models related to superconductivity in cuprates. The same problem has received significant attention because of its connection to very recent experiments of the dynamics of ultra-cold atoms in optical lattices where models of strongly correlated electrons can be simulated. In this paper we apply the diagrammatic Monte Carlo method to calculate the single-hole Green’s function in the t–J model, where the J term is linearized, in a wide range of imaginary-time with the aim to examine the polaron formation and in particular the details of the contribution of the so-called string excitations found in such recent experiments. We calculate the single-hole spectral function by analytic continuation from imaginary to real time and study the various aspects that constitute the string picture, such as, the energy–momentum dependence of the main quasiparticle peak and its residue, the internal excitations of the string which appear as multiple peaks in the spectral function as well as their momentum dependence. We find that the earlier analysis of the spectral function based on a mobile-hole connected with a string of overturn spins and the contribution of the internal string excitations as obtained from the non-crossing approximation is accurate.
We have calculated the hole-hole correlation function for two holes doped into a S=1/2 antiferromagnetic insulator described by the t-J model on a 16-site \ensuremath{\surd}8\ifmmode\times\else\texttimes\fi{}\ensuremath{\surd}32 lattice and a 24-site \ensuremath{\surd}18\ifmmode\times\else\texttimes\fi{}\ensuremath{\surd}32 lattice using an exact diagonalization technique. We predict that the carriers described by this model, in the parameter range relevant to CuO2{\mathrm{CuO}}_{2}CuO2​ planes, tend to stay as far apart as possible. This result is in direct contradiction to previously published exact diagonalization data [e.g., D. Poilblanc, Phys. Rev. B 49, 1477 (1994)]. We suggest that if the carriers do tend to stay as far apart from one another as possible, then the electron momentum distribution function shows evidence for hole pockets at k\ensuremath{\rightarrow}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), consistent with many recent studies of these models, including recent photoemission work.