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AIP conference proceedings

Two-Dimensional t-J Model in a Staggered Field

Yasuhiro Saiga

Published Jan 1, 2003• 0 citations
Publisher

Abstract

The two‐dimensional t‐J model in a staggered field is studied by exact diagonalization up to 20 sites. For the low‐hole‐density region and a realistic value of J/t, it is found that the presence of a staggered field strengthens the attraction between two holes. With increasing field, the dx2−y2‐wave superconducting correlations are enhanced while the extended‐s‐wave ones hardly change. This implies that coexistence of the dx2−y2‐wave superconducting order and the commensurate antiferromagnetic order occurs in a staggered field.

DOI
10.1063/1.1612403

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The two‐dimensional t‐J model in a staggered field is studied by exact diagonalization up to 20 sites. For the low‐hole‐density region and a realistic value of J/t, it is found that the presence of a staggered field strengthens the attraction between two holes. With increasing field, the dx2−y2‐wave superconducting correlations are enhanced while the extended‐s‐wave ones hardly change. This implies that coexistence of the dx2−y2‐wave superconducting order and the commensurate antiferromagnetic order occurs in a staggered field.
The two-dimensional $t\ensuremath{-}J$ model in a staggered field is studied by exact diagonalization of small clusters. For the low-hole-density region and a realistic value of J/t,J/t,J/t, it is found that the presence of a staggered field strengthens the attraction between two holes. With increasing field, the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconducting correlations are enhanced while the extended-s-wave ones hardly change. This implies that coexistence of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconducting order and the commensurate antiferromagnetic order occurs in a staggered field.
The coexisting phase of the d-wave superconducting and the antiferromagnetic order in the two-dimensional t-JJJ model is reexamined using a variational Monte Carlo method in order to estimate the Gutzwiller factors. A trial wave function is used which is consistent with the mean-field solution. The Gutzwiller factors are determined by comparing the numerically obtained expectation values with the mean-field values. We find the z component of the Gutzwiller factor of exchange interaction is enhanced compared with the xy\mathrm{xy}xy components. This effect does not appear in the conventional Gutzwiller approximation and is essential for the stabilization of the antiferromagnetic order in the presence of d-wave superconductivity. We discuss several applications of the present Gutzwiller factors to the problems with antiferromagnetism and d-wave superconductivity.
We examine the influence of a staggered magnetic field on states involving a few holes in the one-dimensional t-J and Hubbard models. We apply exact diagonalizations of small systems, an analytical treatment of an anisotropic model, and a high-field perturbation expansion. Our results suggest that even modest staggered fields, h\ensuremath{\ll}t, induce the formation of bound hole pairs in a broad range of parameters, in particular for J/t1 in the t-J model and for U/t>1 in the Hubbard model. In the same regions, by studying the density-density correlations and the compressibility, we argue that many holes form a paired state and that phase separation does not occur.
Based on the known phenomenology of high-Tc cuprates and the available numerical calculations of the t − J model, a two-dimensional effective fermionic model with the nearest neighbor attraction is proposed. Numerical calculations suggest that the model has the dx2−y2 superconductivity (SC) in the ground state at a low fermionic density. We argue that this model captures the important physics of the dx2−y2 superconducting correlations found earlier in the t − J model by the exact diagonalization approach. Within a self-consistent RPA diagrammatic study, the density and the coupling strength dependence of the critical temperature is calculated. We also investigate the influence of the impurities on our results and show that the suppression of the superconductivity is insignificant, when the retardation effects are accounted for as opposed to the Hartree–Fock approximation.
We study the ``t-J'' model with strongly correlated electrons (infinite-U Hubbard-model kinetic energy plus superexchange J) by exact diagonalization on small two-dimensional clusters of six, eight, and twelve sites on a square lattice with periodic boundary conditions. We find an attractive pairing potential for two holes when J/t\ensuremath{\ge}(J/t)c{)}_{\mathit{c}})c​\ensuremath{\simeq}0.2, with t the hopping matrix element. Ground-state calculations show that extended s-wave and d-wave pairing susceptibilities and equal-time pairing correlations grow weakly with increasing J and system size at fixed filling n. Pairing correlations may be enhanced for (J/t)>(J/t)c{)}_{\mathit{c}})c​\ensuremath{\approxeq}0.2. We compare equal-time pairing correlations to a mean-field theory for J=0 and note potential difficulties with interpreting numerical results for such small systems. The widths of one- and two-hole energy bands in low-spin states are of order J; the one-hole effective mass is larger than the two-hole effective mass in such states. Spin-charge correlation functions for a single hole in the eight- and twelve-site lattices are consistent with the spin-charge decoupling scenario for resonating-valence-bond states.