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Journal of Physics Condensed Matter

Disordered ground-state properties of a double-layer Heisenberg antiferromagnet

Guozhu Wei, An Du

Published Nov 13, 1995• 6 citations
Publisher

Abstract

The disordered ground-state properties of a double-layer quantum antiferromagnet are investigated in the bond operator representation. The intralayer and interlayer couplings are J and J perpendicular to , respectively. In a mean-field approximation, we obtain a spin gap which decreases with increasing ratio lambda =J/J perpendicular to and disappears at the value lambda c =0.292. In the region 0<or= lambda <or= lambda c , we calculate the disordered ground-state energy, the intralayer and interlayer nearest-neighbour singlet strengths, and the correlation length.

DOI
10.1088/0953-8984/7/46/011

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The disordered ground-state properties of a double-layer quantum antiferromagnet are investigated in the bond operator representation. The intralayer and interlayer couplings are J and J perpendicular to , respectively. In a mean-field approximation, we obtain a spin gap which decreases with increasing ratio lambda =J/J perpendicular to and disappears at the value lambda c =0.292. In the region 0<or= lambda <or= lambda c , we calculate the disordered ground-state energy, the intralayer and interlayer nearest-neighbour singlet strengths, and the correlation length.
The double-layer antiferromagnetic quantum XXZ model is studied by the bond-operator mean-field theory. The transverse and longitudinal modes in excited spectra, and the phase diagram for disorder–order phase transition about Δ and J/J⟂, which are the relative strength of spin anisotropy and the ratio of the intralayer coupling to the interlayer coupling, respectively, are obtained. It is found that the critical ratio of (J/J⟂)c is 0.174 for XY model (Δ = 0), and is 0.430 for isotropic model (Δ = 1). In the disordered phase and on the critical points, the excitation spectra are analyzed. The spin gap from the condensed spin singlets to the first excited states, the ground state energy and the spin wave velocities in the disordered state are calculated as functions of parameters Δ and J/J⟂.
We present an exact diagonalization study on layered J1−J2J_{1}-J_{2}J1​−J2​ antiferromagnetic Heisenberg spin model to examine the role of frustration induced by inplane next-nearest neighbor coupling J2J_{2}J2​, in presence of interlayer antiferromagnetic coupling J⊥J_{\perp}J⊥​. A finite lattice of 24 spins in layered geometry of (4×3)⊕(4×3)(4\times 3)\oplus (4\times 3)(4×3)⊕(4×3) is considered and the resulting Hamiltonian matrix diagonalized using Davidson iterative algorithm to obtain the ground and a few low-lying excited states. The lattice size (242424 spins with Hilbert space dimensionality of 270415627041562704156 in Sztot=0S_{z}^{tot}=0Sztot​=0 subspace) has been kept relatively small because of the large number of runs required to sample J1−J2−J⊥J_{1}-J_{2}-J_{\perp}J1​−J2​−J⊥​ parameter space. Quantities like spin-gap, Shannon entropy, spin-spin correlation, static spin structure-factor, magnetic specific-heat and magnetic susceptibility are calculated for various values of spin-spin coupling parameters. With increase in interlayer coupling, the system is driven to states with long range order and the interval of quantum paramagnetically disordered state, sandwiched between Néel and collinear ordered states, narrows on the scale of inplane frustration parameter.
Ground state properties, dispersion relations and scaling behaviour of spin gap of a bond alternating spin-1 2 anisotropic Heisenberg chain have been studied where the exchange interactions on alternate bonds are ferromagnetic (FM) and antiferromagnetic (AFM) in two separate cases.The resulting models separately represent nearest neighbour (NN) AFM-AFM and AFM-FM bond alternating chains.Ground state energy has been estimated analytically by using both bond operator and Jordan-Wigner representations and numerically by using exact diagonalization.Dispersion relations, spin gap and several ground state orders have been obtained.Dimer order and string orders are found to coexist in the ground state.Spin gap is found to develop as soon as the non-uniformity in alternating bond strength is introduced in the AFM-AFM chain which further remains non-zero for the AFM-FM chain.This spin gap along with the string orders attribute to the Haldane phase.The Haldane phase is found to exist in most of the anisotropic region similar to the isotropic point.
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 dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2 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.
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Using the coupled cluster method for high orders of approximation and complementary exact diagonalization studies we investigate the ground state properties of the spin-1/2 J1−−J2{J}_{1}--{J}_{2}J1​−−J2​ frustrated Heisenberg antiferromagnet on the square lattice. We have calculated the ground state energy, the magnetic order parameter, the spin stiffness, and several generalized susceptibilities to probe magnetically disordered quantum valence-bond phases. We have found that the quantum critical points for both the N\'eel and collinear orders are ${J}_{2}^{c1}\ensuremath{\approx}(0.44\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$ and ${J}_{2}^{c2}\ensuremath{\approx}(0.59\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$, respectively, which are in good agreement with the results obtained by other approximations. In contrast to the recent study by [Sirker et al. Phys. Rev. B 73, 184420 (2006)], our data do not provide evidence for the transition from the N\'eel to the valence-bond solid state to be first order. Moreover, our results are in favor of the deconfinement scenario for that phase transition. We also discuss the nature of the magnetically disordered quantum phase.