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Journal of the Physical Society of Japan

Ground-State Properties of Two-Dimensionalt-t'-JModel

Akiharu Miyanaga, Yasumasa Hasegawa, Hidetoshi Fukuyama

Published Apr 15, 1994• 2 citations
Publisher

Abstract

Ground states of the two-dimensional t - t '- J model with one and two holes in 4×4 sites (with periodic boundary conditions) are studied numerically. Using a Lanczos algorithm, we calculate the ground-state energy and momentum distribution, and the phase diagram in the plane of J / t and t '/ t is presented. The momentum distribution for J / t =0.25 is compared with the Fermi surface obtained in the mean-field theory. It is shown that the t '/ t dependences of the momentum distribution are consistent with the mean-field approximation, although there are quantitative differences between them.

DOI
10.1143/jpsj.63.1268

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Ground states of the two-dimensional t - t '- J model with one and two holes in 4×4 sites (with periodic boundary conditions) are studied numerically. Using a Lanczos algorithm, we calculate the ground-state energy and momentum distribution, and the phase diagram in the plane of J / t and t '/ t is presented. The momentum distribution for J / t =0.25 is compared with the Fermi surface obtained in the mean-field theory. It is shown that the t '/ t dependences of the momentum distribution are consistent with the mean-field approximation, although there are quantitative differences between them.
The t ′ and t ′′ -dependences of the dynamical spin correlation function S ( q , ω) of the 2D t - t ′ - t ′′ - J model are studied numerically based on the Lanczos algorithm for two holes on 4 ×4 sites. In particular the spin excitations at q =( π, π) ≡ q 0 are examined in detail and compared with results of the mean-field theory. The spin excitations turned out to be drastically different between YBCO( t ′ =-0.17, t ′′ =0.2) and YBCO(II)( t ′ =-0.5, t ′′ =0)-type, although both types reproduce the similar Fermi surfaces of YBCO and have the similar S ( q 0 , ω) in the mean-field theory. Further understanding of the properties of spin excitation for these two choices of t ′ and t ′′ are pursued by calculating the momentum distribution in the excited states. The spin excitations S ( q 0 , ω) for YBCO(II)-type are shown to be of collective type, while those for YBCO appear to be mainly individual.
Strongly correlated 2D electrons described by the t–J model are investigated numerically. Exact ground state for one and two holes in a finite cluster with periodic boundary conditions are obtained by using the Lanczos algorithm. The effects of Coulomb repulsion of the holes on the nearest neighbor sites are taken into account. Commensurate flux phases are investigated for the same size of clusters. They are shown to be a good approximation for the ground state specially in the intermediate value of J/t.
The evolution of the Fermi surface upon hole doping is studied in the t-J model of correlated electrons by exact diagonalization of chains and planes. In one dimension at low hole doping, the momentum distribution function n(k) indicates the presence of pocketlike features at the (noninteracting) Fermi momentum, while increasing the density of holes a large Fermi surface is observed. Although the results in two dimensions are consistent with this picture, conclusive evidence for the existence of hole pockets (at intermediate doping levels) cannot be provided in the present study of 4\ifmmode\times\else\texttimes\fi{}4 and \ensuremath{\surd}18 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}18 square lattices. In order to improve the resolution in momentum space, twisted boundary conditions are used for the two-dimensional clusters.
Two-dimensional t-J model is studied by a variational Monte Carlo method, using Gutzwiller-Jastrow-type wave functions. Various kinds of superconducting pairing symmetries are compared in order to determine the phase diagram of the ground state in the full J/t-n plane. Near the half filling where the high temperature superconductivity is expected, the d_{x^2-y^2} wave pairing state is always the most stable among various symmetries. The three-site term hardly changes the phase diagram in this regime. In the low electron density, the extended s-type wave becomes a quantitatively good state for large J/t, although the energy gain is small. The Gutzwiller wave function is shown to be the exact ground state in the low-electron-density limit for the supersymmetric case (J/t=2).
We study the momentum distribution function n(k) for the two-dimensional t-J model by high-temperature expansions. Starting with a k-independent n(k) at T=\ensuremath{\infty}, we observe the buildup of a sharp Fermi-surface-like feature as the temperature is lowered. For very small density of electrons, our results are clearly consistent with Luttinger's theorem. At all fillings the contours of constant n(k) closely resemble those of the tight-binding model. No evidence for pocketlike Fermi surfaces is seen. Far from the Fermi surface n(k) has a particle-hole asymmetry similar to that found in the one-dimensional, U=\ensuremath{\infty} Hubbard model.