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Physical review. B, Condensed matter

Electron-momentum distribution and spectral function for two holes in finite-clustert-Jmodels

R. Eder, P. Wróbel

Published Mar 1, 1993• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.47.6010

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We calculate the single-particle excitation spectrum of holes in the Emery model thereby extending and improving previous calculations. The system is considered at half filling (${\mathit{n}}_{\mathit{h}}$=1, one hole per ${\mathrm{CuO}}_{2}$ unit) and for hole doping, where the on-site hole-hole repulsions are kept finite. A paramagnetic form of the ground state is used. For the determination of the retarded Green's functions of copper and oxygen holes, the projection technique is applied solving the resulting equations of motions self-consistently. At half filling, the excitation spectrum exhibits a charge-transfer gap bounded by Zhang-Rice singlet states and the upper Hubbard band. Upon hole doping the flat singlet band crosses the Fermi level giving rise to a large Fermi surface at a hole concentration of ${\mathit{n}}_{\mathit{h}}$=1.25. Moreover, spectral weight is shifted from the upper Hubbard band to the states near the Fermi energy. The calculated spectral densities, the singlet dispersion for the doped system, and the transfer of spectral weight are in good quantitative agreement with exact diagonalization results for 2\ifmmode\times\else\texttimes\fi{}2 ${\mathrm{CuO}}_{2}$ cluster.

Physical review. B, Condensed matter•Dec 1, 1993•49 citations
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.
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 binding energy of two holes with antiparallel spin in the t-J model using a variational wave function based on the string or spin-bag picture. The symmetry of the bound state is dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2. Although the size of matrices to be diagonalized is only 3\ifmmode\times\else\texttimes\fi{}3 we could reproduce the results of various extensive numerical calculations with reasonable accuracy. We show that a sizeable contribution of the binding energy is due to the quantum fluctuations in the ground state of the Heisenberg antiferromagnet. In contrast to exact diagonalization results on small clusters in the thermodynamical limit the binding energy decreases rapidly with increasing t/J. A detailed discussion of the various finite-size effects in a small cluster is also included.
We investigate the effect of doping in the hole spectral function by exact diagonalization of a 16-site cluster with two holes. It is shown that for more than one hole the spectral function differs qualitatively from the one in the single-hole limit. In particular, we find no evidence for the formation of a Fermi surface having hole ``pockets'' localized around (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) in momentum space. On the contrary, a large low-energy peak appears in the spectral function of the hole propagator at k=(\ensuremath{\pi},0) or (0,\ensuremath{\pi}) which is then the best candidate for the existence of those pockets. A (\ensuremath{\pi}/2,\ensuremath{\pi}/2) quasihole state is obtained as a small energy excitation of the two-hole system. We discuss some consequences for photoemission and optical-conductivity experiments in high-Tc{\mathit{T}}_{\mathit{c}}Tc​ materials at intermediate doping.
We present an exact diagonalization study of the doping dependence of the single-particle Green's function in 16-, 18-, and 20-site clusters of the t-J model. We find evidence for the validity of the rigid-band picture starting from the half-filled case: upon doping, the topmost states of the quasiparticle band observed in the photoemission spectrum at half-filling cross the chemical potential and reappear as the lowermost states of the inverse photoemission spectrum. Features in the inverse photoemission spectra, which are inconsistent with the rigid-band picture, are shown to originate from the nontrivial point-group symmetry of the ground state with two holes, which enforces different selection rules than at half-filling. Deviations from rigid-band behavior which lead to the formation of a large Fermi surface in the momentum distribution are found to occur at energies far from the chemical potential. A Luttinger Fermi surface and a nearest-neighbor hopping band do not exist.
We have calculated S(q) and the single particle distribution function 〈nq{\mathit{n}}_{\mathbf{q}}nq​〉 for N holes in the t-J model on a nonsquare \ensuremath{\surd}8 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}32 16-site lattice with periodic boundary conditions. We justify the use of this lattice by appealing to results obtained from the conventional 4\ifmmode\times\else\texttimes\fi{}4 16-site cluster, and an undoped 32-site system, each having the full square symmetry of the bulk. This new cluster has a high density of k points along the diagonal of reciprocal space, viz. along k=k(1,1). The results clearly demonstrate that when the single-hole problem has a ground state with a system momentum of k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2), the resulting ground state for N holes involves a shift of the peak of the system's structure factor away from the antiferromagnetic state q=(\ensuremath{\pi},\ensuremath{\pi}). This shift effectively increases continuously with N. When the single hole problem has a ground state with a momentum that is not equal to k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2), something that may easily be accomplished through the use of the t-t'-J model with t'/t small and positive, then the above-mentioned incommensurability for N holes is not found---the maximum of S(q) remains at q=(\ensuremath{\pi},\ensuremath{\pi}) for all N.The existence of the incommensurate ground states are presented in conjunction with the electron and hole momentum distribution functions. Our results may be interpreted as evidence for rigid-band filling of the dipolar spin distortion states of Shraiman and Siggia---by studying the hole-hole correlation function we demonstrate that the holes on our cluster tend to stay as far apart as is possible, and thus rigid-band filling is not unexpected. Thus, these results demonstrate that in some instances important results for moderately doped CuO2{\mathrm{CuO}}_{2}CuO2​ planes can be predicted from a knowledge of the properties of weakly doped planes. However, the electron Fermi surface that we obtain also satisfies Luttinger's theorem, and has dimples at the wave vectors of the single hole ground state, k=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2). Finally, we comment on the relation of all of these results to the incommensurability found in S(q).
We calculate the single-particle excitation spectrum of holes in the Emery model thereby extending and improving previous calculations. The system is considered at half filling (nh{\mathit{n}}_{\mathit{h}}nh​=1, one hole per CuO2{\mathrm{CuO}}_{2}CuO2​ unit) and for hole doping, where the on-site hole-hole repulsions are kept finite. A paramagnetic form of the ground state is used. For the determination of the retarded Green's functions of copper and oxygen holes, the projection technique is applied solving the resulting equations of motions self-consistently. At half filling, the excitation spectrum exhibits a charge-transfer gap bounded by Zhang-Rice singlet states and the upper Hubbard band. Upon hole doping the flat singlet band crosses the Fermi level giving rise to a large Fermi surface at a hole concentration of nh{\mathit{n}}_{\mathit{h}}nh​=1.25. Moreover, spectral weight is shifted from the upper Hubbard band to the states near the Fermi energy. The calculated spectral densities, the singlet dispersion for the doped system, and the transfer of spectral weight are in good quantitative agreement with exact diagonalization results for 2\ifmmode\times\else\texttimes\fi{}2 CuO2{\mathrm{CuO}}_{2}CuO2​ cluster.