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arXiv:cond-mat/0303587 · Physical review. B, Condensed matter

Dynamical structure factor of the anisotropic Heisenberg chain in a transverse field

Jean-Sébastien Caux, Fabian H. L. Eßler, U. Löw

Published Oct 20, 2003• 63 citations
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Abstract

We consider the anisotropic Heisenberg spin-1/2 chain in a transverse magnetic field at zero temperature. We first determine all components of the dynamical structure factor by combining exact results with a mean-field approximation recently proposed by Dmitriev et al. [JETP 95, 538 (2002)]. We then turn to the small anisotropy limit, in which we use field theory methods to obtain exact results. We discuss the relevance of our results to neutron scattering experiments on the one-dimensional Heisenberg chain compound ${\mathrm{Cs}}_{2}{\mathrm{CoCl}}_{4}.$

DOI
10.1103/physrevb.68.134431

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We calculate dynamical structure factors of the S=1S=1S=1 bond-alternating Heisenberg chain with a single-ion anisotropy in transverse magnetic fields, using a continued fraction method based on the Lanczos algorithm. In the Haldane-gap phase and the dimer phase, dynamical structure factors show characteristic field dependence. Possible interpretations are discussed in the viewpoint of the field dependence of the excitation continuum. The numerical results are in qualitative agreement with recent results for inelastic neutron-scattering experiments on the S=1S=1S=1 bond-alternating Heisenberg-chain compound Ni(C9D24N4)(NO2)ClO4\mathrm{Ni}({\mathrm{C}}_{9}{\mathrm{D}}_{24}{\mathrm{N}}_{4})(\mathrm{N}{\mathrm{O}}_{2})\mathrm{Cl}{\mathrm{O}}_{4}Ni(C9​D24​N4​)(NO2​)ClO4​ and the S=1S=1S=1 Haldane-gap compound Ni(C5D14N2)2N3(PF6)\mathrm{Ni}{({\mathrm{C}}_{5}{\mathrm{D}}_{14}{\mathrm{N}}_{2})}_{2}{\mathrm{N}}_{3}(\mathrm{P}{\mathrm{F}}_{6})Ni(C5​D14​N2​)2​N3​(PF6​) in transverse magnetic fields.
The research presented here focuses on the theoretical investigation of spinons in quasi one-dimensional quantum spin chains from the perspective of neutron scattering, with emphasis placed on the calculation of dynamic spin structure factors for both unpolarised and polarised incident neutrons. Two anisotropic versions of the Heisenberg spin chain are considered for such an examination: the spin-1/21/21/2 antiferromagnetic XXZXXZXXZ model and the spin-1/21/21/2 ferromagnetic XYZXYZXYZ model.The XYZXYZXYZ model supports spinon scattering (modelled at finite temperature) and is related to the so-called Villain mode. The introduction of a perturbation in the form of an external transverse magnetic field or Dzyaloshinskii-Moriya interaction (DMI) leads to the emergence of incommensurability in the system; such a result is a signature of fractional excitations. The presence of these interactions also give rise to a chiral response associated with the spinons in the polarised term of the scattering cross section. The inelastic scattering cross section is computed for both unpolarised and polarised neutrons.In relation to the antiferromagnetic XXZXXZXXZ model, emphasis is on spinon pair creation (modelled at T=0rmKT = 0 {rm K}T=0rmK). Motivated by the presence of a chiral response in the case of the XYZXYZXYZ model mentioned above, a new technique is developed in order to incorporate DMI and the transverse magnetic field so that one can determine if there is a chiral property associated with the two-spinon system. This technique is numerical in nature and is based on Green function methods. Using the results produced by the Green function approach, the inelastic cross section in the presence of an external transverse magnetic field is computed for the first time. The result is compared with experimental neutron scattering data; good agreement is demonstrated between theory and experiments on rmCsCoBr3{rm CsCoBr}_3rmCsCoBr3​.Finally, the Green function approach is generalised to account for the interactions between spin chains in magnetic compounds described by a staggered field. Various dynamic structure factors are computed for this scenario with results compared to experiment; good agreement between the theory and experiments on rmRbCoCl3{rm RbCoCl}_3rmRbCoCl3​ is shown.
We consider the easy-plane anisotropic spin-12\frac{1}{2}21​ Heisenberg chain in combined uniform longitudinal and transverse staggered magnetic fields. The low-energy limit of his model is described by the sine-Gordon quantum field theory. Using methods of integrable quantum field theory we determine the various components of the dynamical structure factor. To do so, we derive explicit expressions for all matrix elements of the low-energy projections of the spin operators involving at most two particles. We discuss applications of our results to experiments on one-dimensional quantum magnets.
We consider the transverse dynamical structure factor of the anisotropic Heisenberg spin-1/2 chain ( XXZ model) in the gapped antiferromagnetic regime (Δ>1). Specializing to the case of zero field, we use two independent approaches based on integrability (one valid for finite size, the other for the infinite lattice) to obtain the exact two-spinon part of this correlator. We discuss in particular its asymmetry with respect to the π/2-momentum line, its overall anisotropy dependence, and its contribution to sum rules.