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Physical review. B, Condensed matter

Effect of environmental spins on quantum coherence in antiferromagnet clusters

Gregory Levine

Published Oct 1, 1997• 3 citations
Publisher

Abstract

The two-dimensional Heisenberg antiferromagnet with an additional isotropic coupling to ``environmental'' spin degrees of freedom is studied by exact diagonalization of small clusters to examine the effect of decoherence from first principles. The dynamical correlation function for the staggered order parameter $c(\ensuremath{\omega})$ is calculated for two systems containing $10$ and $18$ electronic spins coupled to two environmental spins. The evolution of spectral weight in the main macroscopic quantum coherence resonance is followed as a function of environmental coupling and spin anisotropy and is discussed in connection with theoretical work on decoherence.

DOI
10.1103/physrevb.56.7815

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The two-dimensional Heisenberg antiferromagnet with an additional isotropic coupling to ``environmental'' spin degrees of freedom is studied by exact diagonalization of small clusters to examine the effect of decoherence from first principles. The dynamical correlation function for the staggered order parameter c(\ensuremathω)c(\ensuremath{\omega})c(\ensuremathω) is calculated for two systems containing 101010 and 181818 electronic spins coupled to two environmental spins. The evolution of spectral weight in the main macroscopic quantum coherence resonance is followed as a function of environmental coupling and spin anisotropy and is discussed in connection with theoretical work on decoherence.
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.
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Macroscopic quantum coherence oscillations of the N\'eel vector are proved to appear in the antiferromagnetic nuclear spin chain of eight 129Xe{}^{129}\mathrm{Xe}129Xe atoms placed on a magnetic surface. The oscillation period at zero temperature is calculated numerically as a function of the chain constant. The environmental decoherence effects at finite temperature are accounted assuming a dipole coupling between the spin chain and the fluctuating magnetic field of the surface. With this coupling the N\'eel vector oscillations are damped by a rate $(N\ensuremath{-}1)/\ensuremath{\tau},$ where N is the number of spins and $\ensuremath{\tau}$ is the relaxation time of a single spin.