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arXiv:1005.0492 · Physical Review B

Low-temperature dynamical structure factor of the two-leg spin- 12 Heisenberg ladder

W. D. Goetze, Una Karahasanovic, Fabian H. L. Eßler

Published Sep 13, 2010• 25 citations
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Abstract

We determine the dynamical structure factor of the two-leg spin-$\frac{1}{2}$ Heisenberg ladder at low temperatures in the regime of strong rung coupling. The dominant feature at zero temperature is the coherent triplon mode. We show that the line shape of this mode broadens in a nonsymmetric way at finite temperatures and that the degree of asymmetry increases with temperature. We also show that at low frequencies, a temperature-induced resonance akin to the Villain mode in the spin-$\frac{1}{2}$ Heisenberg Ising chain emerges.

DOI
10.1103/physrevb.82.104417

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The zero-temperature dynamical spin-spin correlation functions are calculated for the spin-12\frac{1}{2}21​ two-leg antiferromagnetic Heisenberg ladder in a magnetic field above the lower critical field Hc1{H}_{c1}Hc1​. The dynamical structure factors are calculated, which exhibit both massless modes and massive excitations. These modes appear in different sectors characterized by the parity in the rung direction and by the momentum in the direction of the chains. The structure factors have power-law singularities at the lower edges of their support. The results are also applicable to the spin-1 Heisenberg chain. The implications are briefly discussed for the various correlation functions and the $\ensuremath{\pi}$ resonance in the SO(5) symmetric ladder model.
We consider the spin-1/2 Heisenberg XXZXXZXXZ chain in the regime of large Ising-type anisotropy $\ensuremath{\Delta}$. By a combination of duality and Jordan-Wigner transformations we derive a mapping to weakly interacting spinless fermions, which represent domain walls between the two degenerate ground states. We develop a perturbative expansion in $1/\ensuremath{\Delta}$ for the transverse dynamical spin structure factor at finite temperatures and in an applied transverse magnetic field. We present a unified description for both the low-energy temperature-activated response and the temperature evolution of the T=0T=0T=0 two-spinon continuum. We find that the two-spinon continuum narrows in energy with increasing temperature. At the same time spectral weight is transferred from the two-spinon continuum to the low-energy intraband scattering continuum, which is strongly peaked around the position of the (single) spinon dispersion (``Villain mode'').
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The energy spectra and low-temperature magnetic properties of two one-dimensional Heisenberg mixed spin (s = 1, 1/2) systems, namely decorated two-leg mixed spin ladders with the lattice topology of polyacene, are studied. The gapless character of the exact excitation energy spectra for both ladder models has been determined. We found numerically that the model with macroscopic ground state spin S0 has gapped excitations with the spin S > S0. This leads to the appearance of an intermediate plateau in field dependence of magnetization at low temperatures. We have shown that the ladder with equal coupling in legs has the maximal size of this plateau at the same coupling in rungs. For a mixed spin ladder model with Ising interactions in legs, the appearance of two intermediate magnetization plateaus at low temperatures and some values of coupling parameters was shown.