The excitation spectrum of the two-chain Heisenberg ladder with antiferromagnetic interactions is studied. Our approach is based on the description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Additional singlet (
S=0) and triplet (
S=1) excitations are found as quasiparticle bound states. Thus it is demonstrated that the spectrum consists of one elementary triplet, one composite triplet, and one composite singlet.
Heisenberg antiferromagnetic spin ``ladders'' (two coupled spin chains) are low-dimensional magnetic systems which for S=1/2 interpolate between half-integer-spin chains, when the chains are decoupled, and effective integer-spin one-dimensional chains in the strong-coupling limit. The spin-1/2 ladder may be realized in nature by vanadyl pyrophosphate, (VO
)2P2O7. In this paper we apply strong-coupling perturbation theory, spin-wave theory, Lanczos techniques, and a Monte Carlo method to determine the ground-state energy and the low-lying excitation spectrum of the ladder. We find evidence of a nonzero spin gap for all interchain couplings ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$>0. A band of spin-triplet excitations above the gap is also analyzed. These excitations are unusual for an antiferromagnet, since their long-wavelength dispersion relation behaves as (k-
k0)2 (in the strong-coupling limit ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\gg}J, where J is the in-chain antiferromagnetic coupling). Their band is folded, with a minimum energy at
k0=\ensuremath{\pi}, and a maximum between
k1=\ensuremath{\pi}/2 (for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=0) and 0 (for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=\ensuremath{\infty}). We also give numerical results for the dynamical structure factor S(q,\ensuremath{\omega}), which can be determined in neutron scattering experiments. Finally, possible experimental techniques for studying the excitation spectrum are discussed.
The excitation spectrum of the two-chain
S=1/2 Heisenberg spin ladder with additional second neighbor frustrating interactions is studied by a variety of techniques. A description, based on a mapping of the model onto a Bose gas of hard-core triplets is used to determine the one- and two-particle excitation spectra. We find that low-lying singlet and triplet bound states are present and their binding energy increases with increasing frustration. In addition, many-particle bound states are found by exact diagonalization and variational methods. We prove that the larger the number of bound particles the larger the binding energy. Thus the excitation spectrum has a complex structure and consists of elementary triplets and composite many-particle singlet and triplet bound states. The composite excitations mix strongly with the elementary ones in the coupling regime where quantum fluctuations are strong. The quantum phase transition, known to take place in this model at critical frustration, is interpreted as a condensation process of (infinitely) large many-particle bound states.
The challenge of one-dimensional systems is to understand their physics beyond the level of known elementary excitations. By high-resolution neutron spectroscopy in a quantum spin-ladder material, we probe the leading multiparticle excitation by characterizing the two-magnon bound state at zero field. By applying high magnetic fields, we create and select the singlet (longitudinal) and triplet (transverse) excitations of the fully spin-polarized ladder, which have not been observed previously and are close analogs of the modes anticipated in a polarized Haldane chain. Theoretical modeling of the dynamical response demonstrates our complete quantitative understanding of these states.
The role of dynamical magnetoelastic coupling in spin-Peierls chains is investigated by numerical and analytical techniques. We show that a Heisenberg spin chain coupled to dynamical optical phonons exhibits a transition towards a spontaneously dimerized state in a wide range of parameter space. The low-energy excitations are characterized as solitons. No binding between solitons occurs in the isolated spin-phonon chain and the dynamical spin structure factor shows a broad magnon dispersion. However, elastic interchain coupling can lead to the formation of bound states.
We present a theory of phonon-assisted optical two-magnon absorption in two-leg spin ladders. Based on the strong intra-rung-coupling limit we show that collective excitations of total spin
S=0,1, and 2 exist outside of the two-magnon continuum. It is demonstrated that the singlet collective state has a clear signature in the optical spectrum.