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arXiv:cond-mat/9504013 · Physical review. B, Condensed matter

Ground-state properties and dynamics of the bilayert-Jmodel

R. Eder, Yutaka Ohta, Sadamichi Maekawa

Published Sep 1, 1995• 15 citations
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Abstract

We present an exact diagonalization study of bilayer clusters of the t-J model. Our results indicate a crossover between two markedly different regimes which occurs when the ratio ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J between interlayer and intralayer exchange constants increases: for small ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J the data suggest the development of three-dimensional antiferromagnetic correlations without appreciable degradation of the intralayer spin order and the ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ hole pairs within the planes persist. For larger values of ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J local singlets along the interlayer bonds dominate, leading to an almost complete suppression of the intralayer spin correlation and the breaking of the intralayer hole pairs. The ground state with two holes in this regime has s-like symmetry. We present data for static spin correlation function, magnetic structure factor, and spin gap. We calculate the momentum distribution and electronic spectral function of the ``local singlet state'' realized for large ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J, and show that it deviates markedly from that of a single layer, making it an implausible candidate for modeling high-temperature superconductors.

DOI
10.1103/physrevb.52.7708

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A phase diagram of two Mott-Hubbard planes interacting with a short-range Coulomb repulsion is presented. Considering the case of equal amount of doping by holes in one layer as electrons in the other, a holon-doublon interlayer exciton formation is shown to be a natural consequence of Coulomb attraction. Quasiparticle spectrum is gapped and incoherent below a critical doping ${\ensuremath{\delta}}_{c}$ due to the formation of excitons. A spin-liquid-insulator (SLI) phase is thus realized without the lattice frustration. The critical value ${\ensuremath{\delta}}_{c}$ sensitively depends on the interlayer interaction strength. In the $t\text{\ensuremath{-}}J$ model description of each layer with the ddd-wave pairing, ${\ensuremath{\delta}}_{c}$ marks the crossover between SLI and ddd-wave superconductor. The SLI phase, despite being nonsuperconducting and charge gapped, still shows an electromagnetic response similar to that of a superfluid due to the exciton transport. Including antiferromagnetic order in the $t\text{\ensuremath{-}}J$ model introduces magnetically ordered phases at low doping and pushes the spin-liquid phase to a larger interlayer interaction strength and higher doping concentrations.
The hole-doped two-dimensional(2D) $t\ensuremath{-}J$ model is studied by exact diagonalization on a $5\ifmmode\times\else\texttimes\fi{}4$ cluster which, unlike the standard tilted-square clusters, can in principle accomodate an antiphase domain wall. For hole concentration 1010%10 and J/t> 0.5J/t>~0.5J/t> 0.5 the ground-state energy/site is lower than the conventional tilted-square $\sqrt{20}\ifmmode\times\else\texttimes\fi{}\sqrt{20}$ cluster. In the ground state two holes form a loosely bound pair pinned to an antiphase domain wall. The dynamical density correlation function shows sharp quasiparticlelike peaks, reminiscent of the ``holons'' in 1D chains, which suggest the existence of solitonlike propagating domain walls. The dynamical correlation function of the bond-singlet operator has a low-energy peak structure characteristic of columnar spin-Peierls order, the dynamical spin-correlation function shows an intense and isolated ``resonance peak'' near $(\ensuremath{\pi},\ensuremath{\pi}).$