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Journal of Physics A Mathematical and General

Two-magnon bound states in an alternating Heisenberg chain

Xuefan Jiang, Hong Chen, D. Y. Xing

Published Apr 27, 2001• 5 citations
Publisher

Abstract

The behaviour of a singlet two-magnon bound state in an S = 1/2 alternating Heisenberg antiferromagnetic chain is investigated by a quantum self-consistent theory with the help of the bosonization technique in the continuum limit approach. The singlet two-magnon bound state exists for any dimerization δ>0 at total momentum q = 0. Its dispersion relation is given analytically in the vicinity of zero momentum. In the case of weak dimerization, the binding energy of the singlet two-magnon bound state monotonically increases with increasing dimerization parameter. Our results are consistent with recent experimental data of CuGeO 3 .

DOI
10.1088/0305-4470/34/18/102

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The behaviour of a singlet two-magnon bound state in an S = 1/2 alternating Heisenberg antiferromagnetic chain is investigated by a quantum self-consistent theory with the help of the bosonization technique in the continuum limit approach. The singlet two-magnon bound state exists for any dimerization δ>0 at total momentum q = 0. Its dispersion relation is given analytically in the vicinity of zero momentum. In the case of weak dimerization, the binding energy of the singlet two-magnon bound state monotonically increases with increasing dimerization parameter. Our results are consistent with recent experimental data of CuGeO 3 .
Motivated by recent measurements on CuGeO3{\mathrm{O}}_{3}O3​, the spectrum of magnetic excitations of an antiferromagnetic S=12S=\frac{1}{2}S=21​ chain with alternating coupling strength is investigated. Wave-vector-dependent magnons and a continuum with square-root behavior at the band edges are found. The spectral density of the continua is calculated. Spin-rotation symmetry fixes the gap of the continuum to be twice the elementary magnon gap. This is in excellent agreement with experimental results. The existence of (anti)bound states of two magnons is predicted: below the continuum a singlet and a triplet, above the continuum a quintuplet.
We use recently developed strong-coupling expansion methods to study the two-particle spectra for the frustrated alternating Heisenberg model, consisting of an alternating nearest neighbor antiferromagnetic exchange and a uniform second neighbor antiferromagnetic exchange. Starting from the limit of weakly coupled dimers, we develop high order series expansions for the effective Hamiltonian in the two-particle subspace. In the limit of a strong applied dimerization, we calculate accurately various properties of singlet and triplet bound states and quintet antibound states. We also develop series expansions for bound state energies in various sectors, which can be extrapolated using standard methods to cases where the external bond alternation goes to zero. We study the properties of singlet and triplet bound states in the latter limit and suggest a crucial role for the bound states in the unbinding of triplets and deconfinement of spin-half excitations.
Using the Bond-Operator Technique (BOT), we have studied the low energy excitation spectrum of a frustrated dimerized antiferromagnetic Heisenberg chain. In particular, we have compared our analytical results with previous Exact Diagonalization (ED) data. Qualitatively, the BOT results are in good agreement with the ED data. And even a very good quantitative agreement is obtained in some parameter region. It is clearly shown that there is only one elementary excitation branch (lowest triplet branch) and that the two other well defined excitations which appear below the continuum, one singlet and one triplet, are bound states of two elementary triplets.
We calculate the dynamical structural factor of the S=1S=1S=1 bond-alternating Heisenberg chain. In the Haldane phase, the lowest excited states form the lower edge of the multimagnon continuum in 0< q< qc0<~q<~{q}_{c}0< q< qc​ and the one-magnon mode in ${q}_{c}<~q<~\ensuremath{\pi}.$ As the system approaches the gapless point, qc{q}_{c}qc​ shifts towards $q=\ensuremath{\pi}$ and the largest integrated intensity of the one-magnon mode is decreased. In the singlet-dimer phase, the one-magnon mode appears in 0< q< qc.0<~q<~{q}_{c}.0< q< qc​. As the bond-alternation becomes strong, qc{q}_{c}qc​ shifts towards $q=\ensuremath{\pi}.$ In the antiferromagnetic-ferromagnetic bond-alternation region with a strong ferromagnetic coupling, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~0.2\ensuremath{\pi}$ and $0.8\ensuremath{\pi}<~q<~\ensuremath{\pi},$ and the one-magnon mode appears in $0.2\ensuremath{\pi}<q<0.8\ensuremath{\pi}.$ The largest integrated intensity of the one-magnon mode is 9393%,93 which is slightly smaller than that in the S=1S=1S=1 Haldane-gap system. We further discuss the dynamical structural factor in connection with the inelastic neutron-scattering experiments.