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Disordered Ground‐State Properties of the Double‐Layer Antiferromagnetic Quantum XXZ Model

An Du, G.Z. Wei

Published Jun 1, 2001• 3 citations
Publisher

Abstract

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⟂.

DOI
10.1002/1521-3951(200106)225:2<477::aid-pssb477>3.0.co;2-#

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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⟂.
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.
We investigate the quantum dynamics of the spins on different Heisenberg antiferromagnetic spin lattice systems. Firstly, we applied the coupled-cluster method to the spin-1/2 antiferromagnetic \emph{XXZ} model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory.Secondly, we study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone Γ(q=0)\Gamma(\mathbf q=0)Γ(q=0) and at the magnetic ordering wavevectors ±[Q=(4π/3,0)]\pm[\mathbf Q= (4\pi/3,0)]±[Q=(4π/3,0)], the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.
We study the zero-temperature phase diagram of the J 1 XXZ – J 2 XXZ Heisenberg model for spin-1 particles on an infinite square lattice interacting via nearest-neighbour ( ) and next-nearest-neighbour ( J 2 >0) bonds. The two bonds have the same XXZ -type anisotropy in spin space. The effects on the quasiclassical Néel-ordered and collinear stripe-ordered states of varying the anisotropy parameter Δ are investigated using the coupled cluster method carried out up to high orders. By contrast with the case for spin- particles studied previously, no intermediate disordered phase between the Néel and collinear stripe phases, for any value of the frustration J 2 / J 1 , for either the z -aligned (Δ>1) or xy -planar-aligned (0≤Δ<1) states, is predicted here. The quantum phase transition is determined as first order for all values of J 2 / J 1 and Δ. The position of the phase boundary J 2 c (Δ) is determined accurately. It is observed to deviate most from its classical position (for all values of Δ>0) at the Heisenberg isotropic point (Δ = 1), where J 2 c (1) = 0.55 ± 0.01. By contrast, at the XY isotropic point (Δ = 0), we find J 2 c (0) = 0.50 ± 0.01. In the Ising limit ( ), as expected.
The two-layer square lattice quantum antiferromagnet with spins 12\frac{1}{2}21​ shows a magnetic order-disorder transition at a critical ratio of the interplane to intraplane couplings. We investigate the dynamics of a single hole in a bilayer antiferromagnet described by a $t\ensuremath{-}J$ Hamiltonian. To model the spin background we propose a ground-state wave function for the undoped system that covers both magnetic phases and includes transverse as well as longitudinal spin fluctuations. The photoemission spectrum is calculated using the spin-polaron picture for the whole range of the ratio of the magnetic couplings. This allows for the study of the hole dynamics on both sides of the magnetic order-disorder transition. For small interplane coupling we find a quasiparticle with properties known from the single-layer antiferromagnet, e.g., the dispersion minimum is at $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2).$ For large interplane coupling the hole dispersion is similar to that of a free fermion (with reduced bandwidth). The crossover between these two scenarios occurs inside the antiferromagnetic phase, which indicates that the hole dynamics is governed by the local environment of the hole.
The ground-state properties and quantum phase transitions (QPTs) of the one-dimensional bond-alternative XXZ model are investigated by the infinite time-evolving block decimation (iTEBD) method. The bond-alternative effects on its ground-state phase diagram are discussed in detail. Once the bond alternation is taken into account, the antiferromagnetic phase (Δ > 1) will be destroyed at a given critical point and change into a disordered phase without nonlocal string order. The QPT is shown to be second-order, and the whole phase diagram is provided. For the ferromagnetic phase region (Δ < −1), the critical point r c always equals 1 (independent of Δ), and the QPT for this case is shown to be first-order. The dimerized Heisenberg model is also discussed, and two disordered phases can be distinguished by with or without nonlocal string orders. Both the bipartite entanglement and the fidelity per site, as two kinds of model-independent measures, are capable of describing all the QPTs in such a quantum model.