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Modern Physics Letters B

WAVEFUNCTION RENORMALIZATION OF ONE HOLE IN A STRONGLY CORRELATED SYSTEM

Padmakar V. Panat, Bishwajyoti Dey, D. G. Kanhere, R. E. Amritkar

Published Oct 30, 1995• 1 citation
Publisher

Abstract

The wavefunction renormalization factor Zk of a hole injected in a half-filled band in a strongly correlated system in two dimensions is evaluated analytically using the extended quasiparticle operator introduced by Dagotto and Schrieffer. A model Hamiltonian for such an extended hole is proposed. We analytically calculate Zk for different parameter values and observe that the Zk value increases as compared with what it would be if a bare hole operator is used. This is in conformity with the numerical observation of Dagotto and Schrieffer.

DOI
10.1142/s0217984995001704

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The wavefunction renormalization factor Zk of a hole injected in a half-filled band in a strongly correlated system in two dimensions is evaluated analytically using the extended quasiparticle operator introduced by Dagotto and Schrieffer. A model Hamiltonian for such an extended hole is proposed. We analytically calculate Zk for different parameter values and observe that the Zk value increases as compared with what it would be if a bare hole operator is used. This is in conformity with the numerical observation of Dagotto and Schrieffer.
In models of strongly correlated electrons the wave-function renormalization Zh{\mathit{Z}}_{\mathit{h}}Zh​ of a hole injected in a half-filled band is small compared to unity. This result reduces the accuracy of numerical and analytical predictions of superconductivity for the Hubbard and related models. A simple method is described to deduce approximate quasiparticle operators whose Zh{\mathit{Z}}_{\mathit{h}}Zh​ is closer to 1 than for the standard bare operators. The method is tested for the t-J model. We find that pairing operators constructed out of these quasiparticles are also considerably improved. For example, at J/t=0.2 an improvement by a factor of 10 or more is expected in the signal of superconductivity in a Monte Carlo simulation if these quasiparticle operators are used rather than the standard bare operators.
A model to describe electronic correlations in energy bands is considered. The model is a generalization of the conventional Hubbard model that allows for the fact that the wave function for two electrons occupying the same Wannier orbital is different from the product of single-electron wave functions. We diagonalize the Hamiltonian exactly on a four-site cluster and study its properties as a function of band filling. The quasiparticle weight is found to decrease and the quasiparticle effective mass to increase as the electronic band filling increases, and spectral weight in one- and two-particle spectral functions is transferred from low to high frequencies as the band filling increases. Quasiparticles at the Fermi energy are found to be more ``dressed'' when the Fermi level is in the upper half of the band (hole carriers) than when it is in the lower half of the band (electron carriers). The effective interaction between carriers is found to be strongly dependent on band filling becoming less repulsive as the band filling increases and attractive near the top of the band in certain parameter ranges. The effective interaction is most attractive when the single-hole carriers are most heavily dressed, and in the parameter regime where the effective interaction is attractive, hole carriers are found to ``undress,'' hence become more like electrons, when they pair. It is proposed that these are generic properties of electronic energy bands in solids that reflect a fundamental electron-hole asymmetry of condensed matter. The relation of these results to the understanding of superconductivity in solids is discussed.
The wave-function renormalization constant Z has been calculated for the one-band Hubbard model on a square lattice. Near half-filling the Hamiltonian has been solved on finite clusters (up to 16\ifmmode\times\else\texttimes\fi{}16) by means of the unrestricted Hartree-Fock (UHF) approximation. Some checks of the UHF results have been made on 4\ifmmode\times\else\texttimes\fi{}4 clusters by means of the Lanczos method for U=\ensuremath{\infty}. At high dilutions (two electrons) exact calculations have been carried out. The ground-state wave functions and energies for the different cases here considered are discussed. The system shows nonconventional behavior (Z=0) near half-filling. For a given value of U, Z vanishes at low dopings, and becomes finite as doping is increased. For very large U the value of Z remains finite for all dopings, excluding half-filling. These results are cast into a plausible phase diagram.
The spectral functions of one hole in the t-J and one-band Hubbard models are calculated using exact diagonalization techniques on small lattices. Results for the t-Jz{\mathit{J}}_{\mathit{z}}Jz​ model are also presented. For the t-J model we found that there is a quasiparticle at the bottom of the hole spectrum with an energy well approximated by Eh{\mathit{E}}_{\mathit{h}}Eh​=-3.17+2.83J0.73{\mathit{J}}^{0.73}J0.73 (for 0.1\ensuremath{\le}J\ensuremath{\le}1.0, t=1) on a 4\ifmmode\times\else\texttimes\fi{}4 lattice. The rest of the spectrum is not incoherent: We identified at least two other peaks following a similar power-law behavior with J. We speculate that the J dependence of the results can be explained by a model where the hole is trapped in a confining potential as in the Ising limit. The bandwidth of the hole is linear in J in the region 0.1\ensuremath{\le}J\ensuremath{\le}0.4 although a power-law behavior is not excluded. The spectral weight of the quasiparticle grows like J0.5{\mathit{J}}^{0.5}J0.5 in the same region. We present new analytical results in the large J/t limit to understand the motion of the hole: In perturbation theory it can be shown that the momentum of the hole at large J/t is k=(\ensuremath{\pi},\ensuremath{\pi}) changing to k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2) at intermediate J/t in agreement with numerical and spin-waves results. We show analytically and numerically that the bandwidth of the quasiparticle is of order t in the large J/t limit. This result corresponds to a spin-liquid state. The one-hole spectral function of the Hubbard model is obtained for lattices with 8 and 10 sites. A quasiparticle is also observed in this case. The bandwidth and the relation with the t-J model are discussed and a comparison with recent Monte Carlo results is made. We also review and extend previous results for the ground-state properties of the t-J model.
We investigate the strong correlation effect in the spinless electron-hole two-band Hubbard model using the dynamical mean-field theory. At half filling, both the renormalization factor ZZZ and the number of conduction electrons (valence holes) ncn_cnc​ decrease with increasing the interband Coulomb interaction UUU down to Z∼0.15Z\sim 0.15Z∼0.15 and nc∼0.1n_c\sim 0.1nc​∼0.1 for $U_c \sim \mbox{bandwidth}$ at which the first-order Lifshitz transition occurs from a correlated semimetal with a large effective mass m∗/m=Z−1m^*/m=Z^{-1}m∗/m=Z−1 to a band insulator with a finite gap due to the Hartree shift. A slight hole doping xxx in the band insulator with a large U>UcU>U_cU>Uc​ yields a remarkable correlated semimetal with Z∼0.1Z\sim 0.1Z∼0.1 at x∼0.01x\sim 0.01x∼0.01, where in-gap states emerge above the valence band top and those weights increase with increasing xxx together with the increase in ZZZ similar to the in-gap states observed in doped Mott insulators.