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arXiv:cond-mat/0211335

Dynamical Structure Factors for the Heisenberg Chain with Alternating Exchange

Marcus Mueller, H.-J. Mikeska

Published Nov 15, 2002• 0 citations
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Abstract

We discuss the transition strength between the disordered ground state and the basic low-lying triplet excitation for the Heisenberg chain with alternating exchange based on series expansions in the interdimer interaction up to tenth order. We demonstrate that the wave vector dependence of the simple dimer approximation is strongly modified in higher orders.

DOI
10.48550/arxiv.cond-mat/0211335

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Progress of Theoretical Physics Supplement•Jan 1, 2005•0 citations
We discuss the transition strength between the disordered ground state and the basic low-lying triplet excitation for the Heisenberg chain with alternating exchange based on series expansions in the interdimer interaction up to tenth order. We demonstrate that the wave vector dependence of the simple dimer approximation is strongly modified in higher orders.
We discuss the transition strength between the disordered ground state and the basic low-lying triplet excitation for interacting dimer materials by presenting theoretical calculations and series expansions as well as inelastic neutron scattering results for the material KCuCl 3 . We describe in detail the features resulting from the presence of two differently oriented dimers per unit cell and show how energies and spectral weights of the resulting two modes are related to each other. We present results from the perturbation expansion in the interdimer interaction strength and thus demonstrate that the wavevector dependence of the simple dimer approximation is modified in higher orders. Explicit results are given in tenth order for dimers coupled in 1D, and in second order for dimers coupled in 3D with application to KCuCl 3 and TlCuCl 3 .
We develop a linked cluster method to calculate the spectral weights of many-particle excitations at zero temperature. The dynamical structure factor is expressed as a sum of ``exclusive'' structure factors, each representing contributions from a given set of excited states. A linked cluster technique to obtain high-order series expansions for these quantities is discussed. We apply these methods to the alternating Heisenberg chain around the dimerized limit $(\ensuremath{\lambda}=0),$ where complete wave vector and frequency-dependent spectral weights for one- and two-particle excitations (continuum and bound states) are obtained. For small to moderate values of the interdimer coupling parameter $\ensuremath{\lambda},$ these lead to extremely accurate calculations of the dynamical structure factors. We also examine the variation of the relative spectral weights of one- and two-particle states with bond alternation all the way up to the limit of the uniform chain $(\ensuremath{\lambda}=1).$ In agreement with Schmidt and Uhrig, we find that the spectral weight is dominated by 2-triplet states even at $\ensuremath{\lambda}=1,$ which implies that a description in terms of triplet-pair excitations remains a good quantitative description of the system even for the uniform chain.
We study the spin-1/2 Heisenberg chain with alternating nearest neighbor interactions ${J}_{1}(1+\ensuremath{\delta})$ and ${J}_{1}(1\ensuremath{-}\ensuremath{\delta})$ and a uniform second neighbor interaction ${J}_{2}=y(1\ensuremath{-}\ensuremath{\delta})$ by series expansions around the limit of decoupled dimers $(\ensuremath{\delta}=1).$ By extrapolating to $\ensuremath{\delta}=0$ and tuning y, we study the critical point separating the power-law and spontaneously dimerized phases of the spin-1/2 antiferromagnet. We then focus on the disorder line y=0.5,y=0.5,y=0.5, $0<~\ensuremath{\delta}<~1,$ where the ground states are known exactly. We calculate the triplet excitation spectrum, their spectral weights, and wave vector dependent static susceptibility along this line. It is well known that as $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\delta}}0,$ the spin gap is still nonzero but the triplets are replaced by spinons as the elementary excitations. We study this dynamical transition by analyzing the series for the spectral weight and the static susceptibility. In particular, we show that the spectral weight for the triplets vanishes and the static spin susceptibility changes from a simple pole at imaginary wave vectors to a branch cut at the transition.
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.
Dynamical structure factors of the S =1 bond-alternating spin chains in the dimer state are calculated at finite temperature using the pair dynamical correlated-effective-field approximation. At T =0, the delta-function-type peak corresponding to the one-magnon mode appears. When temperature increases, such a sharp peak is broadened and the additional weak peak caused by the excitation from the triplet state to the quintet state emerges in the higher energy region. The results are discussed in comparison with those obtained by the exact diagonalization method.